On the power graph of a monogenic semigroup

Let S-M = {0, x, x(2), ... , x(n)} be a monogenic semigroup with zero. Here, we consider the power graph P(S-M) over S-M with vertex set S-M(*) = SM\{0} and two distinct vertices x(i) and x(j) are adjacent if i divides j or j divides i, where 1 <= i, j <= n. We compute various graph parameters of P(S-M) and topological indices based on distance of vertices. Finally, we compute some graph parameters of the cartesian product P(S-M(1)) rectangle P(S-M(2)) of graphs P(S-M(1)) and P(S-M(2)).