The Wiener Index of an Undirected Power Graph

The undirected power graph P(Z_n) of a finite group Z_n is the graph with vertex set G and two distinct vertices u and v are adjacent if and only if u ≠ v and or . The Wiener index W(P(Z_n)) of an undirected power graph P(Z_n) is defined to be sum of distances between all unordered pair of vertices in P(Z_n). Similarly, the edge-Wiener index W_e(P(Z_n)) of P(Z_n) is defined to be the sum of distances between all unordered pairs of edges in P(Z_n). In this paper, we concentrate on the wiener index of a power graph , P(Z_pq) and P(Z_p). Firstly, we obtain new results on the wiener index and edge-wiener index of power graph P(Z_n), using m,n and Euler function. Also, we obtain an equivalence between the edge-wiener index and wiener index of a power graph of Z_n.