Domination polynomial of the commuting and noncommuting graphs of some finite nonabelian groups

A dominating set S of a graph is a subset of the vertex set of the graph in which the closed neighborhood of S is the whole vertex set. A domination polynomial of a graph contains coefficients that represent the number of dominating sets in the graph. A domination polynomial is usually being obtaine...

Full description

Saved in:
Bibliographic Details
Main Authors: Najmuddin, Nabilah, Sarmin, Nor Haniza, Erfanian, Ahmad
Format: Conference Proceeding
Language:English
Subjects:
Apexes
Commuting
Graphs
Polynomials
Quaternions
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:A dominating set S of a graph is a subset of the vertex set of the graph in which the closed neighborhood of S is the whole vertex set. A domination polynomial of a graph contains coefficients that represent the number of dominating sets in the graph. A domination polynomial is usually being obtained for common types of graphs but not for graphs associated to groups. Two types of graphs associated to groups that are used in this research are the commuting graph and the noncommuting graph. The commuting graph of a group G is a graph whose vertex set contains all noncentral elements of G and any two vertices in the set are adjacent if and only if they commute in G. Meanwhile, the noncommuting graph of a group G is a graph whose vertex set contains all noncentral elements of G and any two vertices in the set are adjacent if and only if they do not commute in G. This paper establishes the domination polynomial of the commuting and noncommuting graphs for the dihedral groups, generalized quaternion groups and quasidihedral groups.
ISSN:0094-243X
1551-7616
DOI:10.1063/1.5136363