g-noncommuting graph of some finite groups

Authors

  • M. Nasiri Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.
  • A. Erfanian Department of Pure Mathematics and Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad, Mashhad, Iran.
  • M. Ganjali Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.
  • A. Jafarzadeh Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.

Keywords:

Non-commuting graph, g-noncommuting graph, connected graph

Abstract

Let GG be a finite non-abelian group and gg a fixed element of GG. In 2014, Tolue et al. introduced the g-noncommuting graph of GG, which was denoted by ΓgGΓGg with vertex set GG and two distinct vertices xx and yy join by an edge if [x,y]≠g[x,y]≠g and g−1g−1. In this paper, we consider induced subgraph of ΓgGΓGg on G/Z(G)G/Z(G) and survey some graph theoretical properties like connectivity, the chromatic and independence numbers of this graph associated to symmetric, alternating and dihedral groups.

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Published

2016-12-31

Issue

Vol. 12 No. 1 (2016): Journal of Prime Research in Mathematics

Section

Regular

How to Cite

g-noncommuting graph of some finite groups. (2016). Journal of Prime Research in Mathematics, 12(1), 16 – 23. https://jprm.sms.edu.pk/index.php/jprm/article/view/117