General Form of Domination Polynomial for Two Types of Graphs Associated to Dihedral Groups

Authors

  • Nabilah Najmuddin Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia
  • Nor Haniza Sarmin Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia
  • Ahmad Erfanian Department of Pure Mathematics, Faculty of Mathematics, Ferdowsi University of Mashhad, Azadi Square, Iran

DOI:

https://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 non-central 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 non-central 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.

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Published

2019-07-31

How to Cite

Najmuddin, N., Sarmin, N. H., & Erfanian, A. (2019). General Form of Domination Polynomial for Two Types of Graphs Associated to Dihedral Groups. MATEMATIKA: Malaysian Journal of Industrial and Applied Mathematics, 35(2), 149–155. https://doi.org/10.11113/matematika.v35.n2.1106

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Articles