The Conjugate and Generalized Conjugacy Class Graphs for Metacyclic 3-Groups and Metacyclic 5-Groups

摘要

Let G be a metacyclic p-group where p is either 3 or 5, and let Q be the set of all ordered pairs (x, y) in GxG such that lcm(|x|,|y|)= p, xy=yx and x ≠ y. In this paper, the conjugate graphs associated to metacyclic 3-groups and metacyclic 5-groups are found. Besides, the generalized conjugacy class graphs of these groups are also determined. We show that the conjugate graphs for both groups are a union complete graph and empty graph. Meanwhile, the generalized conjugacy class graphs for both groups are complete and null graph.