**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**14

# graph Related Publications

##### 14 Terminal Wiener Index for Graph Structures

**Authors:**
J. Baskar Babujee,
J. Senbagamalar

**Abstract:**

The topological distance between a pair of vertices i and j, which is denoted by d(vi, vj), is the number of edges of the shortest path joining i and j. The Wiener index W(G) is the sum of distances between all pairs of vertices of a graph G. W(G) = i

**Keywords:**
Distance,
tree,
graph,
degree,
wiener index,
Pendent vertex

##### 13 Sign Pattern Matrices that Admit P0 Matrices

**Authors:**
Ting-Zhu Huang,
Ling Zhang

**Abstract:**

A P0-matrix is a real square matrix all of whose principle minors are nonnegative. In this paper, we consider the class of P0-matrix. Our main aim is to determine which sign pattern matrices are admissible for this class of real matrices.

**Keywords:**
graph,
digraph,
Sign pattern matrices,
P0 matrices

##### 12 On Fractional (k,m)-Deleted Graphs with Constrains Conditions

**Authors:**
Sizhong Zhou,
Hongxia Liu

**Abstract:**

Let G be a graph of order n, and let k 2 and m 0 be two integers. Let h : E(G) [0, 1] be a function. If e∋x h(e) = k holds for each x V (G), then we call G[Fh] a fractional k-factor of G with indicator function h where Fh = {e E(G) : h(e) > 0}. A graph G is called a fractional (k,m)-deleted graph if there exists a fractional k-factor G[Fh] of G with indicator function h such that h(e) = 0 for any e E(H), where H is any subgraph of G with m edges. In this paper, it is proved that G is a fractional (k,m)-deleted graph if (G) k + m + m k+1 , n 4k2 + 2k − 6 + (4k 2 +6k−2)m−2 k−1 and max{dG(x), dG(y)} n 2 for any vertices x and y of G with dG(x, y) = 2. Furthermore, it is shown that the result in this paper is best possible in some sense.

**Keywords:**
graph,
degree condition,
fractional k-factor,
fractional (k,
m)-deleted graph

##### 11 Fuzzy Adjacency Matrix in Graphs

**Authors:**
Mahdi Taheri,
Mehrana Niroumand

**Abstract:**

**Keywords:**
graph,
adjacency matrix,
fuzzy numbers

##### 10 Distributed Load Flow Analysis using Graph Theory

**Authors:**
D. P. Sharma,
A. Chaturvedi,
G.Purohit,
R.Shivarudraswamy

**Abstract:**

**Keywords:**
graph,
array,
radial distribution network,
Load-flow

##### 9 Notes on Fractional k-Covered Graphs

**Authors:**
Sizhong Zhou,
Yang Xu

**Abstract:**

**Keywords:**
graph,
fractional k-factor,
binding number,
fractional k-covered graph

##### 8 A Neighborhood Condition for Fractional k-deleted Graphs

**Authors:**
Sizhong Zhou,
Hongxia Liu

**Abstract:**

Abstract–Let k ≥ 3 be an integer, and let G be a graph of order n with n ≥ 9k +3- 42(k - 1)2 + 2. Then a spanning subgraph F of G is called a k-factor if dF (x) = k for each x ∈ V (G). A fractional k-factor is a way of assigning weights to the edges of a graph G (with all weights between 0 and 1) such that for each vertex the sum of the weights of the edges incident with that vertex is k. A graph G is a fractional k-deleted graph if there exists a fractional k-factor after deleting any edge of G. In this paper, it is proved that G is a fractional k-deleted graph if G satisfies δ(G) ≥ k + 1 and |NG(x) ∪ NG(y)| ≥ 1 2 (n + k - 2) for each pair of nonadjacent vertices x, y of G.

**Keywords:**
graph,
fractional k-factor,
minimum degree,
neighborhood union,
fractional k-deleted graph

##### 7 Evaluation of a Bio-Mechanism by Graphed Static Equilibrium Forces

**Authors:**
A.Y. Bani Hashim,
N.A. Abu Osman,
W.A.B. Wan Abas,
L. Abdul Latif

**Abstract:**

The unique structural configuration found in human foot allows easy walking. Similar movement is hard to imitate even for an ape. It is obvious that human ambulation relates to the foot structure itself. Suppose the bones are represented as vertices and the joints as edges. This leads to the development of a special graph that represents human foot. On a footprint there are point-ofcontacts which have contact with the ground. It involves specific vertices. Theoretically, for an ideal ambulation, these points provide reactions onto the ground or the static equilibrium forces. They are arranged in sequence in form of a path. The ambulating footprint follows this path. Having the human foot graph and the path crossbred, it results in a representation that describes the profile of an ideal ambulation. This profile cites the locations where the point-of-contact experience normal reaction forces. It highlights the significant of these points.

**Keywords:**
Foot,
graph,
edge,
Ambulation,
vertex

##### 6 [a, b]-Factors Excluding Some Specified Edges In Graphs

**Authors:**
Sizhong Zhou,
Bingyuan Pu

**Abstract:**

Let G be a graph of order n, and let a, b and m be positive integers with 1 ≤ a<b. An [a, b]-factor of G is deﬁned as a spanning subgraph F of G such that a ≤ dF (x) ≤ b for each x ∈ V (G). In this paper, it is proved that if n ≥ (a+b−1+√(a+b+1)m−2)2−1 b and δ(G) > n + a + b − 2 √bn+ 1, then for any subgraph H of G with m edges, G has an [a, b]-factor F such that E(H)∩ E(F) = ∅. This result is an extension of thatof Egawa [2].

**Keywords:**
graph,
minimum degree,
b]-factor

##### 5 Hamiltonian Factors in Hamiltonian Graphs

**Authors:**
Sizhong Zhou,
Bingyuan Pu

**Abstract:**

**Keywords:**
Neighborhood,
graph,
factor,
Hamiltonian factor

##### 4 A Sufficient Condition for Graphs to Have Hamiltonian [a, b]-Factors

**Authors:**
Sizhong Zhou

**Abstract:**

Let a and b be nonnegative integers with 2 ≤ a < b, and let G be a Hamiltonian graph of order n with n ≥ (a+b−4)(a+b−2) b−2 . An [a, b]-factor F of G is called a Hamiltonian [a, b]-factor if F contains a Hamiltonian cycle. In this paper, it is proved that G has a Hamiltonian [a, b]-factor if |NG(X)| > (a−1)n+|X|−1 a+b−3 for every nonempty independent subset X of V (G) and δ(G) > (a−1)n+a+b−4 a+b−3 .

**Keywords:**
Neighborhood,
graph,
minimum degree,
b]-factor,
Hamiltonian [a

##### 3 Automatic Fingerprint Classification Using Graph Theory

**Authors:**
Mana Tarjoman,
Shaghayegh Zarei

**Abstract:**

Using efficient classification methods is necessary for automatic fingerprint recognition system. This paper introduces a new structural approach to fingerprint classification by using the directional image of fingerprints to increase the number of subclasses. In this method, the directional image of fingerprints is segmented into regions consisting of pixels with the same direction. Afterwards the relational graph to the segmented image is constructed and according to it, the super graph including prominent information of this graph is formed. Ultimately we apply a matching technique to compare obtained graph with the model graphs in order to classify fingerprints by using cost function. Increasing the number of subclasses with acceptable accuracy in classification and faster processing in fingerprints recognition, makes this system superior.

**Keywords:**
Fingerprint,
classification,
graph,
Directional image,
Super graph

##### 2 Another Formal Proposal For Stealth

**Authors:**
Adrien Derock,
Pascal Veron

**Abstract:**

**Keywords:**
Detection,
graph,
eradication,
stealth,
rootkit

##### 1 Intention Recognition using a Graph Representation

**Authors:**
Kyung-Whan Oh,
So-Jeong Youn

**Abstract:**

**Keywords:**
HCI,
Intention Recognition,
graph,
intention