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Paper   IPM / M / 16716
School of Mathematics
  Title:   On the regular graph related to G-conjugacy classes
  Author(s):  Zeinab Akhlaghi (Joint with Sh. Rahimi)
  Status:   Published
  Journal: Bull. Aust. Math. Soc.
  Year:  2021
  Pages:   DOI: 10.1017/S0004972721000368
  Supported by:  IPM
Given a finite group G with a normal subgroup N, the simple graph ΓG( N ) is a graph whose vertices are of the form |xG|, where xN\Z(G), and xG is the G-conjugacy class of N containing the element x. Two vertices |xG| and |yG| are adjacent if they are not co-prime. In this article we prove that, if ΓG(N) is a connected incomplete regular graph, then N = P ×A where P is a p-group, for some prime p, AZ(G), and Z(N)\not = NZ(G).

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