The Laplacian Energy of Conjugacy Class Graph of Some Finite Groups

Authors

  • Rabiha Mahmoud Department of Mathematical Sciences, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Malaysia
  • Amira Fadina Ahmad Fadzil Department of Mathematical Sciences, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Malaysia
  • Nor Haniza Sarmin Department of Mathematical Sciences, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Malaysia
  • Ahmad Erfanian Department of Pure Mathematics, Faculty of Mathematical Sciences, and Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad, Mashhad, Iran

DOI:

https://doi.org/10.11113/matematika.v35.n1.1059

Abstract

Let G be a dihedral group and its conjugacy class graph. The Laplacian energy of the graph, is defined as the sum of the absolute values of the difference between the Laplacian eigenvalues and the ratio of twice the edges number divided by the vertices number. In this research, the Laplacian matrices of the conjugacy class graph of some dihedral groups, generalized quaternion groups, quasidihedral groups and their eigenvalues are first computed. Then, the Laplacian energy of the graphs are determined.

Author Biography

Nor Haniza Sarmin, Department of Mathematical Sciences, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Malaysia

A Professor of Mathematics, Department of Mathematical Sciences, Faculty of science. Universiti Teknologi Malaysia.

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Published

2019-04-01

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Articles