Journal of Physics Conference Series, Volume (1988), No (1), Year (2021-7) , Pages (12072-12081)

Title : ( Independence polynomial of the commuting and noncommuting graphs associated to the quasidihedral group )

Authors: Nabilah Najmuddin , Nor Haniza Sarmin , Ahmad Erfanian ,

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Abstract

An independence polynomial is a type of graph polynomial from graph theory that store combinatorial information such as the graph properties or graph invariants. The independence polynomial of a graph contains coefficients that represent the number of independent sets of certain sizes and the degree of the polynomial denotes the independence number of the graph. A graph of group G is called commuting graph if the vertices are noncentral elements of G and two vertices are adjacent if and only if they commute in G. Meanwhile, a noncommuting graph of a group G has a vertex set that contains all noncentral elements of G and two vertices are adjacent if and only if they do not commute in G. Since the group properties can be presented as graph from graph theory, then the graph polynomial of such graph should also be identified. Therefore, in this research, the independence polynomials are determined for the commuting and noncommuting graphs that are associated to the quasidihedral group.

Keywords

Graph polynomial; independence polynomial; graph theory; group theory
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@article{paperid:1088655,
author = {Nabilah Najmuddin and Nor Haniza Sarmin and Erfanian, Ahmad},
title = {Independence polynomial of the commuting and noncommuting graphs associated to the quasidihedral group},
journal = {Journal of Physics Conference Series},
year = {2021},
volume = {1988},
number = {1},
month = {July},
issn = {1742-6588},
pages = {12072--12081},
numpages = {9},
keywords = {Graph polynomial; independence polynomial; graph theory; group theory},
}

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%0 Journal Article
%T Independence polynomial of the commuting and noncommuting graphs associated to the quasidihedral group
%A Nabilah Najmuddin
%A Nor Haniza Sarmin
%A Erfanian, Ahmad
%J Journal of Physics Conference Series
%@ 1742-6588
%D 2021

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