![Sample our Mathematics & Statistics journals, sign in here to start your FREE access for 14 days]({"type":"image" , "src" : "/sda/5943/TOC-Subject-Sample-2021-Mathematics-Statistics.jpg"})
Abstract
The power graph 
of a semigroup S is a simple graph with vertex set S and two distinct vertices x and y are adjacent if and only if xm = y or ym = x for some positive integer m. If m is a fixed positive integer, say k, then it is called k-power graph of S and it is denoted by 
. In this paper we study the structures of the components of 
for the multiplicative semigroup 
. We also study connectedness, cycle structures and symmetry of 
for a cyclic group Hn of order n. Finally applying some of these results we find structures and conditions for symmetries of k-power graphs of dihedral and dicyclic groups.
Keywords:
Mathematics Subject Classification: