Conditions on the Edges and Vertices of Non-commuting Graph


  • M. Jahandideh Department of Mathematics, College of Polymer, Mahshahr Branch, Islamic Azad University, Mahshahr, Iran
  • M. R. Darafsheh School of Mathematics College of Science, University of Tehran, Tehran, Iran
  • N. H. Sarmin Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia
  • S. M. S. Omer Department of Mathematics, Faculty of Science, Benghazi University, Libya



Finite group, non-commuting graph


Abstract - Let G􀡳 be a non- abelian finite group. The non-commuting graph ,􀪡is defined as a graph with a vertex set􀡳 − G-Z(G)􀢆in which two vertices x􀢞 and y􀢟 are joined if and only if xy􀢞􀢟 ≠ yx􀢟􀢞.  In this paper, we invest some results on the number of edges set , the degree of avertex of non-commuting graph and the number of conjugacy classes of a finite group. In order that if 􀪡􀡳non-commuting graph of H ≅ non - commuting graph of G􀪡􀡴,H 􀡴 is afinite group, then |G􀡳| = |H􀡴| .


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