Search results for: graphs andgroups.

Authors: Walter Hussak, Heiko Schröder

Abstract:

Star graphs are Cayley graphs of symmetric groups of permutations, with transpositions as the generating sets. A star graph is a preferred interconnection network topology to a hypercube for its ability to connect a greater number of nodes with lower degree. However, an attractive property of the hypercube is that it has a Hamiltonian decomposition, i.e. its edges can be partitioned into disjoint Hamiltonian cycles, and therefore a simple routing can be found in the case of an edge failure. The existence of Hamiltonian cycles in Cayley graphs has been known for some time. So far, there are no published results on the much stronger condition of the existence of Hamiltonian decompositions. In this paper, we give a construction of a Hamiltonian decomposition of the star graph 5-star of degree 4, by defining an automorphism for 5-star and a Hamiltonian cycle which is edge-disjoint with its image under the automorphism.

Keywords: interconnection networks, paths and cycles, graphs andgroups.

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Authors: Bahadir O. Guler, Serkan Kader, Murat Besenk

Abstract:

In this paper we examine some properties of suborbital graphs for the congruence subgroup r 0 (N) . Then we give necessary and sufficient conditions for graphs to have triangels.

Keywords: Congruence subgroup, Imprimitive action, Modulargroup, Suborbital graphs.

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Authors: A.Nagoor Gani, J.Malarvizhi

Abstract:

In this paper, the order, size and degree of the nodes of the isomorphic fuzzy graphs are discussed. Isomorphism between fuzzy graphs is proved to be an equivalence relation. Some properties of self complementary and self weak complementary fuzzy graphs are discussed.

Keywords: complementary fuzzy graphs, co-weak isomorphism, equivalence relation, fuzzy relation, weak isomorphism.

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Authors: Y. Wang

Abstract:

The Traveling salesman problem (TSP) is NP-hard in combinatorial optimization. The research shows the algorithms for TSP on the sparse graphs have the shorter computation time than those for TSP according to the complete graphs. We present an improved iterative algorithm to compute the sparse graphs for TSP by frequency graphs computed with frequency quadrilaterals. The iterative algorithm is enhanced by adjusting two parameters of the algorithm. The computation time of the algorithm is O(CN_maxn²) where C is the iterations, N_max is the maximum number of frequency quadrilaterals containing each edge and n is the scale of TSP. The experimental results showed the computed sparse graphs generally have less than 5n edges for most of these Euclidean instances. Moreover, the maximum degree and minimum degree of the vertices in the sparse graphs do not have much difference. Thus, the computation time of the methods to resolve the TSP on these sparse graphs will be greatly reduced.

Keywords: Frequency quadrilateral, iterative algorithm, sparse graph, traveling salesman problem.

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Authors: Robert Gold

Abstract:

Control flow graphs are a well-known representation of the sequential control flow structure of programs with a multitude of applications. Not only single functions but also sets of functions or complete programs can be modeled by control flow graphs. In this case the size of the graphs can grow considerably and thus makes it difficult for software engineers to analyze the control flow. Graph reductions are helpful in this situation. In this paper we define reductions to subsets of nodes. Since executions of programs are represented by paths through the control flow graphs, paths should be preserved. Furthermore, the composition of reductions makes a stepwise analysis approach possible.

Keywords: Control flow graph, graph reduction.

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Authors: T. Pathinathan, M. Peter

Abstract:

Fuzzy graphs incorporate concepts from graph theory with fuzzy principles. In this paper, we make a study on the properties of fuzzy graphs which are non-cyclic and are of two-dimensional in structure. In particular, this paper presents 2D structure or the structure of double layer for a non-cyclic fuzzy graph whose underlying crisp graph is non-cyclic. In any graph structure, introducing 2D structure may lead to an inherent cycle. We propose relevant conditions for 2D structured non-cyclic fuzzy graphs. These conditions are extended even to fuzzy graphs of the 3D structure. General theoretical properties that are studied for any fuzzy graph are verified to 2D structured or double layered fuzzy graphs. Concepts like Order, Degree, Strong and Size for a fuzzy graph are studied for 2D structured or double layered non-cyclic fuzzy graphs. Using different types of fuzzy graphs, the proposed concepts relating to 2D structured fuzzy graphs are verified.

Keywords: Double layered fuzzy graph, double layered non-cyclic fuzzy graph, strong, order, degree and size.

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Authors: Swapnil Gupta, C. Pandu Rangan

Abstract:

A uniquely restricted matching is defined to be a matching M whose matched vertices induces a sub-graph which has only one perfect matching. In this paper, we make progress on the open question of the status of this problem on interval graphs (graphs obtained as the intersection graph of intervals on a line). We give an algorithm to compute maximum cardinality uniquely restricted matchings on certain sub-classes of interval graphs. We consider two sub-classes of interval graphs, the former contained in the latter, and give O(|E|^2) time algorithms for both of them. It is to be noted that both sub-classes are incomparable to proper interval graphs (graphs obtained as the intersection graph of intervals in which no interval completely contains another interval), on which the problem can be solved in polynomial time.

Keywords: Uniquely restricted matching, interval graph, design and analysis of algorithms, matching, induced matching, witness counting.

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Authors: Ashish Goswami, Rakesh Sharma

Abstract:

In this paper, LDPC Codes based on defected fullerene graphs have been generated. And it is found that the codes generated are fast in encoding and better in terms of error performance on AWGN Channel.

Keywords: LDPC Codes, Fullerene Graphs, Defected Fullerene Graphs.

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Authors: Khidir R. Sharaf, Didar A. Ali

Abstract:

The nullity η(G) of a graph is the occurrence of zero as an eigenvalue in its spectra. A zero-sum weighting of a graph G is real valued function, say f from vertices of G to the set of real numbers, provided that for each vertex of G the summation of the weights f(w) over all neighborhood w of v is zero for each v in G.A high zero-sum weighting of G is one that uses maximum number of non-zero independent variables. If G is graph with an end vertex, and if H is an induced subgraph of G obtained by deleting this vertex together with the vertex adjacent to it, then, η(G)= η(H). In this paper, a high zero-sum weighting technique and the endvertex procedure are applied to evaluate the nullity of t-tupple and generalized t-tupple graphs are derived  and determined for some special types of graphs,

 Also, we introduce and prove some important results about the t-tupple coalescence, Cartesian and Kronecker products of nut graphs.

Keywords: Graph theory, Graph spectra, Nullity of graphs.

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Authors: S.K.Ayyaswamy, S.Balachandran

Abstract:

The Detour matrix (DD) of a graph has for its ( i , j) entry the length of the longest path between vertices i and j. The DD-eigenvalues of a connected graph G are the eigenvalues for its detour matrix, and they form the DD-spectrum of G. The DD-energy EDD of the graph G is the sum of the absolute values of its DDeigenvalues. Two connected graphs are said to be DD- equienergetic if they have equal DD-energies. In this paper, the DD- spectra of a variety of graphs and their DD-energies are calculated.

Keywords: Detour eigenvalue (of a graph), detour spectrum(of a graph), detour energy(of a graph), detour - equienergetic graphs.

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Authors: Xiaohua Liu, Juan F. Beltran, Nishant Mohanchandra, Godfried T. Toussaint

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Support vector machines (SVMs) are considered to be the best machine learning algorithms for minimizing the predictive probability of misclassification. However, their drawback is that for large data sets the computation of the optimal decision boundary is a time consuming function of the size of the training set. Hence several methods have been proposed to speed up the SVM algorithm. Here three methods used to speed up the computation of the SVM classifiers are compared experimentally using a musical genre classification problem. The simplest method pre-selects a random sample of the data before the application of the SVM algorithm. Two additional methods use proximity graphs to pre-select data that are near the decision boundary. One uses k-Nearest Neighbor graphs and the other Relative Neighborhood Graphs to accomplish the task.

Keywords: Machine learning, data mining, support vector machines, proximity graphs, relative-neighborhood graphs, k-nearestneighbor graphs, random sampling, training data condensation.

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Authors: C.Natarajan, S.K.Ayyaswamy

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Let G be a fuzzy graph. Then D Ôèå V is said to be a strong (weak) fuzzy dominating set of G if every vertex v ∈ V -D is strongly (weakly) dominated by some vertex u in D. We denote a strong (weak) fuzzy dominating set by sfd-set (wfd-set). The minimum scalar cardinality of a sfd-set (wfd-set) is called the strong (weak) fuzzy domination number of G and it is denoted by γsf (G)γwf (G). In this paper we introduce the concept of strong (weak) domination in fuzzy graphs and obtain some interesting results for this new parameter in fuzzy graphs.

Keywords: Fuzzy graphs, fuzzy domination, strong (weak) fuzzy domination number.

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Authors: Shin-Shin Kao, Yuan-Kang Shih, Hsun Su

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In this paper, we show that the conjecture of Chv tal, which states that any 1-tough graph is either a Hamiltonian graph or its complement contains a specific graph denoted by F, does not hold in general. More precisely, it is true only for graphs with six or seven vertices, and is false for graphs with eight or more vertices. A theorem is derived as a correction for the conjecture.

Keywords: Complement, degree sum, Hamiltonian, tough.

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Authors: Maryam Hsaini, Mostafa Nouri-Baygi

Abstract:

A critical problem in wireless sensor networks is limited battery and memory of nodes. Therefore, each node in the network could maintain only a subset of its neighbors to communicate with. This will increase the battery usage in the network because each packet should take more hops to reach its destination. In order to tackle these problems, spanner graphs are defined. Since each node has a small degree in a spanner graph and the distance in the graph is not much greater than its actual geographical distance, spanner graphs are suitable candidates to be used for the topology of a wireless sensor network. In this paper, we study Yao graphs and their behavior for a randomly selected set of points. We generate several random point sets and compare the properties of their Yao graphs with the complete graph. Based on our data sets, we obtain several charts demonstrating how Yao graphs behave for a set of randomly chosen point set. As the results show, the stretch factor of a Yao graph follows a normal distribution. Furthermore, the stretch factor is in average far less than the worst case stretch factor proved for Yao graphs in previous results. Furthermore, we use Yao graph for a realistic point set and study its stretch factor in real world.

Keywords: Wireless sensor network, spanner graph, Yao Graph.

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Authors: H. Y. Pourali, V. V. Joshi, B. N. Waphare.

Abstract:

In this paper, we verify the diameter of zero divisor graphs with respect to direct product.

Keywords: Atomic lattice, complement of graph, diameter, direct product of lattices, 0-distributive lattice, girth, product of graphs, prime ideal, zero divisor graph.

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Authors: H. V. Chen

Abstract:

Assume that we have m identical graphs where the graphs consists of paths with k vertices where k is a positive integer. In this paper, we discuss certain labelling of the m graphs called c-Erdösian for some positive integers c. We regard labellings of the vertices of the graphs by positive integers, which induce the edge labels for the paths as the sum of the two incident vertex labels. They have the property that each vertex label and edge label appears only once in the set of positive integers {c, . . . , c+6m- 1}. Here, we show how to construct certain c-Erdösian of m paths with 2 and 3 vertices by using Skolem sequences.

Keywords: c-Erdösian, Skolem sequences, magic labelling

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Authors: R. Anitha, R. S. Lekshmi

Abstract:

Graph decompositions are vital in the study of combinatorial design theory. Given two graphs G and H, an H-decomposition of G is a partition of the edge set of G into disjoint isomorphic copies of H. An n-sun is a cycle Cn with an edge terminating in a vertex of degree one attached to each vertex. In this paper we have proved that the complete graph of order 2n, K2n can be decomposed into n-2 n-suns, a Hamilton cycle and a perfect matching, when n is even and for odd case, the decomposition is n-1 n-suns and a perfect matching. For an odd order complete graph K2n+1, delete the star subgraph K1, 2n and the resultant graph K2n is decomposed as in the case of even order. The method of building n-suns uses Walecki's construction for the Hamilton decomposition of complete graphs. A spanning tree decomposition of even order complete graphs is also discussed using the labeling scheme of n-sun decomposition. A complete bipartite graph Kn, n can be decomposed into n/2 n-suns when n/2 is even. When n/2 is odd, Kn, n can be decomposed into (n-2)/2 n-suns and a Hamilton cycle.

Keywords: Hamilton cycle, n-sun decomposition, perfectmatching, spanning tree.

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Authors: Jeffrey L. Duffany

Abstract:

Graph coloring is an important problem in computer science and many algorithms are known for obtaining reasonably good solutions in polynomial time. One method of comparing different algorithms is to test them on a set of standard graphs where the optimal solution is already known. This investigation analyzes a set of 50 well known graph coloring instances according to a set of complexity measures. These instances come from a variety of sources some representing actual applications of graph coloring (register allocation) and others (mycieleski and leighton graphs) that are theoretically designed to be difficult to solve. The size of the graphs ranged from ranged from a low of 11 variables to a high of 864 variables. The method used to solve the coloring problem was the square of the adjacency (i.e., correlation) matrix. The results show that the most difficult graphs to solve were the leighton and the queen graphs. Complexity measures such as density, mobility, deviation from uniform color class size and number of block diagonal zeros are calculated for each graph. The results showed that the most difficult problems have low mobility (in the range of .2-.5) and relatively little deviation from uniform color class size.

Keywords: graph coloring, complexity, algorithm.

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Authors: Pranav Ravikumar, Arunabha Bera, Vijay K. Mehra, Anand Kumar

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This paper solves the Non Linear Schrodinger Equation using the Split Step Fourier method for modeling an optical fiber. The model generates a complex wave of optical pulses and using the results obtained two graphs namely Loss versus Wavelength and Dispersion versus Wavelength are generated. Taking Chromatic Dispersion and Polarization Mode Dispersion losses into account, the graphs generated are compared with the graphs formulated by JDS Uniphase Corporation which uses standard values of dispersion for optical fibers. The graphs generated when compared with the JDS Uniphase Corporation plots were found to be more or less similar thus verifying that the model proposed is right. MATLAB software was used for doing the modeling.

Keywords: Modulation, Non Linear Schrodinger Equation, Optical fiber, Split Step Fourier Method.

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Authors: Matthias Dehmer, Frank Emmert Streib, Alexander Mehler, Jürgen Kilian, Max Mühlhauser

Abstract:

Due to the tremendous amount of information provided by the World Wide Web (WWW) developing methods for mining the structure of web-based documents is of considerable interest. In this paper we present a similarity measure for graphs representing web-based hypertext structures. Our similarity measure is mainly based on a novel representation of a graph as linear integer strings, whose components represent structural properties of the graph. The similarity of two graphs is then defined as the optimal alignment of the underlying property strings. In this paper we apply the well known technique of sequence alignments for solving a novel and challenging problem: Measuring the structural similarity of generalized trees. In other words: We first transform our graphs considered as high dimensional objects in linear structures. Then we derive similarity values from the alignments of the property strings in order to measure the structural similarity of generalized trees. Hence, we transform a graph similarity problem to a string similarity problem for developing a efficient graph similarity measure. We demonstrate that our similarity measure captures important structural information by applying it to two different test sets consisting of graphs representing web-based document structures.

Keywords: Graph similarity, hierarchical and directed graphs, hypertext, generalized trees, web structure mining.

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Authors: Azze-Eddine Maredj, Nourredine Tonkin

Abstract:

The recent developments in computing and communication technology permit to users to access multimedia documents with variety of devices (PCs, PDAs, mobile phones...) having heterogeneous capabilities. This diversification of supports has trained the need to adapt multimedia documents according to their execution contexts. A semantic framework for multimedia document adaptation based on the conceptual neighborhood graphs was proposed. In this framework, adapting consists on finding another specification that satisfies the target constraints and which is as close as possible from the initial document. In this paper, we propose a new way of building the conceptual neighborhood graphs to best preserve the proximity between the adapted and the original documents and to deal with more elaborated relations models by integrating the relations relaxation graphs that permit to handle the delays and the distances defined within the relations.

Keywords: Conceptual Neighborhood Graph, Relaxation Graphs, Relations with Delays, Semantic Adaptation of Multimedia Documents.

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Authors: Fangfang Chen, Chunlu Wang, Zhihong Tian, Shuyuan Jin, Tianle Zhang

Abstract:

Attack graph is an integral part of modeling the overview of network security. System administrators use attack graphs to determine how vulnerable their systems are and to determine what security measures to deploy to defend their systems. Previous methods on AGG(attack graphs generation) are aiming at the whole network, which makes the process of AGG complex and non-scalable. In this paper, we propose a new approach which is simple and scalable to AGG by decomposing the whole network into atomic domains. Each atomic domain represents a host with a specific privilege. Then the process for AGG is achieved by communications among all the atomic domains. Our approach simplifies the process of design for the whole network, and can gives the attack graphs including each attack path for each host, and when the network changes we just carry on the operations of corresponding atomic domains which makes the process of AGG scalable.

Keywords: atomic domain, vulnerability, attack graphs, generation, computer security

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Authors: Udaya Kumar Reddy K. R, K. Viswanathan Iyer

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Given a simple connected unweighted undirected graph G = (V (G), E(G)) with |V (G)| = n and |E(G)| = m, we present a new algorithm for the all-pairs shortest-path (APSP) problem. The running time of our algorithm is in O(n2 log n). This bound is an improvement over previous best known O(n2.376) time bound of Raimund Seidel (1995) for general graphs. The algorithm presented does not rely on fast matrix multiplication. Our algorithm with slight modifications, enables us to compute the APSP problem for unweighted directed graph in time O(n2 log n), improving a previous best known O(n2.575) time bound of Uri Zwick (2002).

Keywords: Distance in graphs, Dynamic programming, Graphalgorithms, Shortest paths.

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Authors: Anthony Spiteri Staines

Abstract:

This paper examines the modeling and analysis of a cruise control system using a Petri net based approach, task graphs, invariant analysis and behavioral properties. It shows how the structures used can be verified and optimized.

Keywords: Software Engineering, Real Time Analysis andDesign, Petri Nets, Task Graphs, Parallelism.

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Authors: Mahdi Taheri, Mehrana Niroumand

Abstract:

In this paper a new definition of adjacency matrix in the simple graphs is presented that is called fuzzy adjacency matrix, so that elements of it are in the form of 0 and n N n 1 , ∈ that are in the interval [0, 1], and then some charactristics of this matrix are presented with the related examples . This form matrix has complete of information of a graph.

Keywords: Graph, adjacency matrix, fuzzy numbers

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Authors: Hsun Su, Yuan-Kang Shih, Shin-Shin Kao

Abstract:

Many well-known interconnection networks, such as kary n-cubes, recursive circulant graphs, generalized recursive circulant graphs, circulant graphs and so on, are shown to belong to the family of cycle composition networks. Recently, various studies about mutually independent hamiltonian cycles, abbreviated as MIHC-s, on interconnection networks are published. In this paper, using an improved construction method, we obtain MIHC-s on cycle composition networks with a much weaker condition than the known result. In fact, we established the existence of MIHC-s in the cycle composition networks and the result is optimal in the sense that the number of MIHC-s we constructed is maximal.

Keywords: Hamiltonian cycle, k-ary n-cube, cycle composition networks, mutually independent.

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Authors: Marek Skomorowski

Abstract:

In syntactic pattern recognition a pattern can be represented by a graph. Given an unknown pattern represented by a graph g, the problem of recognition is to determine if the graph g belongs to a language L(G) generated by a graph grammar G. The so-called IE graphs have been defined in [1] for a description of patterns. The IE graphs are generated by so-called ETPL(k) graph grammars defined in [1]. An efficient, parsing algorithm for ETPL(k) graph grammars for syntactic recognition of patterns represented by IE graphs has been presented in [1]. In practice, structural descriptions may contain pattern distortions, so that the assignment of a graph g, representing an unknown pattern, to a graph language L(G) generated by an ETPL(k) graph grammar G is rejected by the ETPL(k) type parsing. Therefore, there is a need for constructing effective parsing algorithms for recognition of distorted patterns. The purpose of this paper is to present a new approach to syntactic recognition of distorted patterns. To take into account all variations of a distorted pattern under study, a probabilistic description of the pattern is needed. A random IE graph approach is proposed here for such a description ([2]).

Keywords: Syntactic pattern recognition, Distorted patterns, Random graphs, Graph grammars.

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Authors: Gabofetswe Malema, Michael Liebelt

Abstract:

LDPC codes could be used in magnetic storage devices because of their better decoding performance compared to other error correction codes. However, their hardware implementation results in large and complex decoders. This one of the main obstacles the decoders to be incorporated in magnetic storage devices. We construct small high girth and rate 2 columnweight codes from cage graphs. Though these codes have low performance compared to higher column weight codes, they are easier to implement. The ease of implementation makes them more suitable for applications such as magnetic recording. Cages are the smallest known regular distance graphs, which give us the smallest known column-weight 2 codes given the size, girth and rate of the code.

Keywords: Structured LDPC codes, cage graphs.

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Authors: Decha Samana, Vites Longani

Abstract:

For positive integer s and t, the Ramsey number R(s, t) is the least positive integer n such that for every graph G of order n, either G contains Ks as a subgraph or G contains Kt as a subgraph. We construct the circulant graphs and use them to obtain lower bounds of some small Ramsey numbers.

Keywords: Lower bound, Ramsey numbers, Graphs, Distance line.

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Authors: Do Phuc, Nguyen Thi Kim Phung

Abstract:

In this paper, we represent protein structure by using graph. A protein structure database will become a graph database. Each graph is represented by a spectral vector. We use Jacobi rotation algorithm to calculate the eigenvalues of the normalized Laplacian representation of adjacency matrix of graph. To measure the similarity between two graphs, we calculate the Euclidean distance between two graph spectral vectors. To cluster the graphs, we use M-tree with the Euclidean distance to cluster spectral vectors. Besides, M-tree can be used for graph searching in graph database. Our proposal method was tested with graph database of 100 graphs representing 100 protein structures downloaded from Protein Data Bank (PDB) and we compare the result with the SCOP hierarchical structure.

Keywords: Eigenvalues, m-tree, graph database, protein structure, spectra graph theory.

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