Assist. Prof. Dr. Abdul Jalil M. Khalaf

Committee: International Scientific Committee of Mathematical and Computational Sciences
University: University of Kufa
Department: Department of Mathematics
Research Fields: Graph Theory, Discrete Mathematics, Applied Mathematics, Topology,

Publications

1 On Chromaticity of Wheels

Authors: Abdul Jalil M. Khalaf, Zainab Yasir Al-Rekaby

Abstract:

Let the vertices of a graph such that every two adjacent vertices have different color is a very common problem in the graph theory. This is known as proper coloring of graphs. The possible number of different proper colorings on a graph with a given number of colors can be represented by a function called the chromatic polynomial. Two graphs G and H are said to be chromatically equivalent, if they share the same chromatic polynomial. A Graph G is chromatically unique, if G is isomorphic to H for any graph H such that G is chromatically equivalent to H. The study of chromatically equivalent and chromatically unique problems is called chromaticity. This paper shows that a wheel W12 is chromatically unique.

Keywords: chromatic polynomial, chromatically equivalent, chromatically unique, wheel

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1658

Abstracts

3 Hosoya Polynomials of Zero-Divisor Graphs

Authors: Abdul Jalil M. Khalaf, Esraa M. Kadhim

Abstract:

The Hosoya polynomial of a graph G is a graphical invariant polynomial that its first derivative at x= 1 is equal to the Wiener index and second derivative at x=1 is equal to the Hyper-Wiener index. In this paper we study the Hosoya polynomial of zero-divisor graphs.

Keywords: wiener index, Hosoya polynomial, Hyper-Wiener index, zero-divisor graphs

Procedia PDF Downloads 340
2 A Study of Chromatic Uniqueness of W14

Authors: Abdul Jalil M. Khalaf, Zainab Yasir Al-Rekaby

Abstract:

Coloring the vertices of a graph such that every two adjacent vertices have different color is a very common problem in the graph theory. This is known as proper coloring of graphs. The possible number of different proper colorings on a graph with a given number of colors can be represented by a function called the chromatic polynomial. Two graphs G and H are said to be chromatically equivalent, if they share the same chromatic polynomial. A Graph G is chromatically unique, if G is isomorphic to H for any graph H such that G is chromatically equivalent to H. The study of chromatically equivalent and chromatically unique problems is called chromaticity. This paper shows that a wheel W14 is chromatically unique.

Keywords: chromatic polynomial, chromatically equivalent, chromatically unique, wheel

Procedia PDF Downloads 273
1 On Chromaticity of Wheels

Authors: Abdul Jalil M. Khalaf, Zainab Yasir Abed Al-Rekaby

Abstract:

Let the vertices of a graph such that every two adjacent vertices have different color is a very common problem in the graph theory. This is known as proper coloring of graphs. The possible number of different proper colorings on a graph with a given number of colors can be represented by a function called the chromatic polynomial. Two graphs G and H are said to be chromatically equivalent, if they share the same chromatic polynomial. A Graph G is chromatically unique, if G is isomorphic to H for any graph H such that G is chromatically equivalent to H. The study of chromatically equivalent and chromatically unique problems is called chromaticity. This paper shows that a wheel W12 is chromatically unique.

Keywords: chromatic polynomial, chromatically equivalent, chromatically unique, wheel

Procedia PDF Downloads 266