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.


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.


Balakrishnan, R., 2004. The Energy of a Graph. Linear Algebra and its Applications, Volume 387, pp. 287-295.
Banci, M., Chillag, D., Herzog, A. & Scoppola, C., 1992. Applications of a Graph Related to Conjugacy Classes in Finite Groups. Arch Math, Volume 58, pp. 126-132.
Bapat, R. & Pati, S., 2004. Energy of Graph is Never an Odd Integer. Bull. Kerala Math. Assoc., Volume 1, pp. 129-132.
Bertram, E. A., Herzog, M. & Mann, A., 1990. On a Graph Related to Conjugacy Classes of Groups. Bull. London Math. Soc, Volume 22, pp. 569-575.
Biggs, N., 1993. Algebraic Graph Theory. 2nd ed. Cambridge Mathematical Press, Cambridge: Cambridge Mathematical Library.
Brouwer, A. E. & Haemers, W. H., 2011. Spectra of Graph. New York: Springer.
Erfanian, A. & Tolue, B., 2012. Conjugate Graphs of Finite Groups. Discret Mathematics and Applicaions, 4(2), pp. 35-43.
Fraleigh, J. B., 2002. A First Course in A bstract Algebra. seventh ed. USA: Addison Wesly Logman, Inc.
Godsil, C. & Royle, G., 2001. Algebraic Graph Theory. Fifth ed. London: Springer-Verlag.
Godstil, C. & Royle, G., 2001. Algebraic Graph Theory. Boston New York: Springer.
Gutman, I., 1978. The Energy of Graph. Der. Math, stat. Sekt. Forschungzent, Volume 103, pp. 1-22.
Prizada, S. & Gutman, I., 2008. The Energy of a Graph is Never Square Root of an Odd Integer. Applicable Analaysts and Discrete Mathematics, Volume 2, pp. 118-121.
Woods, C., 2013. Favorite Application Using Graph Eigenvalues: Graph Engenery. Volume 17, pp. 535-538.
Yu, A., Lu, M. & and Tian, F., 2004. New Apper Bounded for The Energy of Graphs. MATCH Commun. Math. Comput. Chem, Volume 53, pp. 441-448.
Zhou, B., 2004. Energy of Graph. MATCH Commun. Math. Comput. Chem, Volume 51, pp. 111-118.
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.