# 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

## Abstracts

##### 3 Hosoya Polynomials of Zero-Divisor Graphs

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

**Abstract:**

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

##### 2 A Study of Chromatic Uniqueness of W14

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

**Abstract:**

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

##### 1 On Chromaticity of Wheels

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

**Abstract:**

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