On the generalized commuting and non-commuting graph for metacyclic 3-groups
Keywords:Metacyclic 3-Groups, Commuting Graph, Non-Commuting Graph, Commute
AbstractLet be a metacyclic 3-group and let be a non-empty subset of such that . The generalized commuting and non-commuting graphs of a group is denoted by and respectively. The vertex set of the generalized commuting and non-commuting graphs are the non-central elements in the set such that where Two vertices in are joined by an edge if they commute, meanwhile, the vertices in are joined by an edge if they do not commute.
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