On the power graphs of certain finite groups

Abstract

ABSTRACT The power graph of a group Ω is a graph, whose node set is Ω and two distinct elements are adjacent if and only if one is an integral power of the other. A metric dimension of a graph Γ, denoted by ψ(Γ) is the minimum cardinality of the resolving set of Γ. In this context, we study distant properties and detour distant properties such as closure, interior, distance degree sequence and eccentric subgraphs of the power graphs of certain finite non-abelian groups. As a consequence, we figure out the metric dimension and resolving polynomial of power graphs for dihedral and generalized quaternion groups by using neighbourhood and twin sets.