Najmuddin, Nabilah and Sarmin, Nor Haniza and Erfanian, Ahmad (2019) General form of domination polynomial for two types of graphs associated to dihedral groups. MATEMATIKA, 35 (Aug). pp. 149155. ISSN 01279602

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Official URL: https://dx.doi.org/10.11113/matematika.v35.n2.1106
Abstract
A domination polynomial is a type of graph polynomial in which its coefficients represent the number of dominating sets in the graph. There are many researches being done on the domination polynomial of some common types of graphs but not yet for graphs associated to finite groups. Two types of graphs associated to finite groups are the conjugate graph and the conjugacy class graph. A graph of a group G is called a conjugate graph if the vertices are noncentral elements of G and two distinct vertices are adjacent if they are conjugate to each other. Meanwhile, a conjugacy class graph of a group G is a graph in which its vertices are the noncentral conjugacy classes of G and two distinct vertices are connected if and only if their class cardinalities are not coprime. The conjugate and conjugacy class graph of dihedral groups can be expressed generally as a union of complete graphs on some vertices. In this paper, the domination polynomials are computed for the conjugate and conjugacy class graphs of the dihedral groups.
Item Type:  Article 

Uncontrolled Keywords:  Domination polynomial, conjugate graph, conjugacy class graph, dihedral group 
Subjects:  Q Science > QA Mathematics 
Divisions:  Science 
ID Code:  84880 
Deposited By:  Fazli Masari 
Deposited On:  29 Feb 2020 12:39 
Last Modified:  29 Feb 2020 12:39 
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