The Wiener Index of an Undirected Power Graph
- 1 Gazi University, Mathematics, Ankara, Turkey
- 2 Gazi University, Mathematics, Ankara, Turkey
Abstract
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 .
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