Ghorbani, M., Gharavi-Alkhansari, Z. (2017). On the energy of non-commuting graphs. Journal of Linear and Topological Algebra (JLTA), 06(02), 135-146.

M. Ghorbani; Z. Gharavi-Alkhansari. "On the energy of non-commuting graphs". Journal of Linear and Topological Algebra (JLTA), 06, 02, 2017, 135-146.

Ghorbani, M., Gharavi-Alkhansari, Z. (2017). 'On the energy of non-commuting graphs', Journal of Linear and Topological Algebra (JLTA), 06(02), pp. 135-146.

Ghorbani, M., Gharavi-Alkhansari, Z. On the energy of non-commuting graphs. Journal of Linear and Topological Algebra (JLTA), 2017; 06(02): 135-146.

^{}Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, 16785-136, Iran

Abstract

For given non-abelian group G, the non-commuting (NC)-graph $\Gamma(G)$ is a graph with the vertex set $G$\ $Z(G)$ and two distinct vertices $x, y\in V(\Gamma)$ are adjacent whenever $xy \neq yx$. The aim of this paper is to compute the spectra of some well-known NC-graphs.

[1] A. Abdollahi, S. Akbari, H. R. Maimani, Non-commuting graph of a group, J. Algebra 298 (2006) 468-492.

[2] M. R. Darafsheh, Groups with the same non-commuting graph, Discrete Appl. Math. 157 (2009) 833-837.

[3] M. Ghorbani, Z. Gharavi-AlKhansari, An algebraic study of non-commuting graphs, Filomat 31 (2017) 663- 669.

[4] I. Gutman, The energy of a graph, Ber. Math. Statist. Sekt. Forschungsz Graz 103 (1978) 1-22.

[5] A. R. Moghaddamfar, W. J. Shi, W. Zhou, A. R. Zokayi, On the non-commuting graph associated with a finite group, Siberian Math. J. 46 (2005) 325-332.

[6] G. L. Morgan, C. W. Parker, The diameter of the commuting graph of a finite group with trivial centre, J. Algebra 393 (2013) 41-59.

[7] B. H. Neumann, A problem of Paul Erd˝os on groups, J. Austral. Math. Soc. Ser. A, 21 (1976) 467-472.