On the minimum degree of the power graph of a finite abelian p-group

The power graph of a group G is a special type of undirected as well as simple graph which is donted by P(G) whose vertex set is G and two distinct vertices u and v are adjacent either u = vn or v = um, where n, m ∈ Z+. The minimum degree δ(P(ℤn)) of P(ℤn) is known when n has only two distinct prime divisors, where ℤn is the cyclic group of order n. In this research article, we are able to identify one such vertex from finite abelian p-group which has minimum degree without any condition.