# The independence polynomial of conjugate graph and noncommuting graph of groups of small order.

## Authors

• Nabilah Najmuddin Universiti Teknologi Malaysia
• Nor Haniza Sarmin Universiti Teknologi Malaysia

## Keywords:

Independence polynomial, conjugate graph, noncommuting graph, nonabelian group

## Abstract

An independent set of a graph is a set of pairwise non-adjacent vertices. The independence polynomial of a graph is defined as a polynomial in which the coefficient is the number of the independent set in the graph.  Meanwhile, a graph of a group G is called conjugate graph if the vertices are non-central elements of G and two distinct vertices are adjacent if they are conjugate. The noncommuting graph is defined as a graph whose vertex set is non-central elements in which two vertices are adjacent if and only if they do not commute. In this research, the independence polynomial of the conjugate graph and noncommuting graph are found for three nonabelian groups of order at most eight.

## Author Biographies

### Nabilah Najmuddin, Universiti Teknologi Malaysia

Candidate, Doctor of Philosophy (Mathematics)Department of Mathematical Sciences,Faculty of Science,Universiti Teknologi Malaysia

### Nor Haniza Sarmin, Universiti Teknologi Malaysia

Professor of Mathematics

Department of Mathematical Sciences,Faculty of Science,Universiti Teknologi Malaysia

Professor of Mathematics

Department of Mathematics and Center of Excellence in Analysis on Algebraic Structures,

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