The Energy of Cayley Graphs for a Generating Subset of the Dihedral Groups

Authors

  • Amira Fadina Ahmad Fadzil Universiti Teknologi Malaysia
  • Nor Haniza Sarmin Universiti Teknologi Malaysia
  • Ahmad Erfanian Ferdowsi University of Mashhad, Iran

DOI:

https://doi.org/10.11113/matematika.v35.n3.1115

Abstract

Let G be a finite group and S be a subset of G where S does not include the identity of G and is inverse closed. A Cayley graph of a group G with respect to the subset S is a graph where its vertices are the elements of G and two vertices a and b are connected if ab^(−1) is in the subset S. The energy of a Cayley graph is the sum of all absolute values of the eigenvalues of its adjacency matrix. In this paper, we consider a specific subset S = {b, ab, . . . , a^(n−1)b} for dihedral group of order 2n, where n is greater or equal to 3 and find the Cayley graph with respect to the set. We also calculate the eigenvalues and compute the energy of the respected Cayley graphs. Finally, the generalization of the energy of the respected Cayley graphs is found.

Author Biographies

Amira Fadina Ahmad Fadzil, Universiti Teknologi Malaysia

PhD Candidate

Department of Mathematical Sciences
Faculty of Science
Universiti Teknologi Malaysia
81310 UTM Johor Bahru
Johor, Malaysia

Ahmad Erfanian, Ferdowsi University of Mashhad, Iran

Department of Pure Mathematics, Faculty of Mathematical Sciences and Center of Excellence in Analysis on Algebraic Structures

Downloads

Published

2019-12-01

Issue

Section

Articles