نوع مقاله : مقاله پژوهشی (کاربردی)
نویسنده
گروه ریاضی، دانشگاه فنی و حرفه ای، تهران، ایران
چکیده
کلیدواژهها
موضوعات
عنوان مقاله [English]
نویسنده [English]
Let G be a finite non-abelian metacyclic p-group (p is an odd prime number) and Z(G) be its center. The non-commuting graph delta(G) of the group G is defined as the graph, whose vertex set is and two distinct vertices u and v are connected by an edge if and only if the commutator of u and v is not the identity. In this paper, the exact number of conjugacy classes of G is obtained, then the various properties of the non-commuting graph of the group are given. Moreover, the number of edges, vertices, the completeness and the connection of the graph are examined. In particular, we prove that the click number and the chromatic number of these graphs are the same. In addition, the centralizers of the group are computed. Also, exact formulas for the centralizer sizes of G are obtained and using these results, the n-th commutativity degrees of such groups in terms of their parameters are computed.
کلیدواژهها [English]
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