The Energy of Conjugacy Classes Graphs of Some Order of Alternating Groups

  • Zuzan Naaman Hassan Mathematics Department, Faculty of Basic Education, University of Raparin, Rania, Kurdistan Region, Iraq.
  • Nihad Titan Sarhan Mathematics Department, College of Education-Akre, Duhok University, Duhok, Kurdistan Region, Iraq.
Keywords: Alternating Group, Conjugacy Class, Conjugacy Class Graph, Energy Of Graph.

Abstract

The energy of a graph , is the sum of all absolute values of the eigen values of the adjacency matrix which is indicated by . An adjacency matrix is a square matrix used to represent of finite graph where the rows and columns consist of 0 or 1-entry depending on the adjacency of the vertices of the graph. The group of even permutations of a finite set is known as an alternating group  . The conjugacy class graph is a graph whose vertices are non-central conjugacy classes of a group , where two vertices are connected if their cardinalities are not coprime. In this paper, the conjugacy class of alternating group  of some order for   and their energy are computed. The Maple2019 software and Groups, Algorithms, and Programming (GAP) are assisted for computations.

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Published
2020-12-04
How to Cite
Hassan, Z., & Sarhan, N. (2020). The Energy of Conjugacy Classes Graphs of Some Order of Alternating Groups. Journal of University of Raparin, 7(4), 62-71. https://doi.org/10.26750/Vol(7).No(4).paper5