Conditions on the Edges and Vertices of Non-commuting Graph
Keywords:Finite group, non-commuting graph
AbstractAbstract - Let Gô€¡³ be a non- abelian finite group. The non-commuting graph ,ô€ª¡is defined as a graph with a vertex setô€¡³ âˆ’ G-Z(G)ô€¢†in which two vertices xô€¢ž and yô€¢Ÿ are joined if and only if xyô€¢žô€¢Ÿ â‰ yxô€¢Ÿô€¢ž. Â 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 ô€ª¡ô€¡³non-commuting graph of H â‰… non - commuting graph of Gô€ª¡ô€¡´,H ô€¡´ is afinite group, then |Gô€¡³| = |Hô€¡´| .
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