TITLE:
The Wiener Index of an Undirected Power Graph
AUTHORS:
Volkan Aşkin, Şerife Büyükköse
KEYWORDS:
Wiener Index, Edge-Wiener Index, An Undirected Power Graph, Line Graph
JOURNAL NAME:
Advances in Linear Algebra & Matrix Theory,
Vol.11 No.1,
March
12,
2021
ABSTRACT: The undirected power graph P(Zn) of a finite group Zn 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(Zn)) of an undirected power graph P(Zn) is defined to be sum of distances between all unordered pair of vertices in P(Zn). Similarly, the edge-Wiener index We(P(Zn)) of P(Zn) is defined to be the sum of distances between all unordered pairs of edges in P(Zn). In this paper, we concentrate on the wiener index of a power graph , P(Zpq) and P(Zp). Firstly, we obtain new results on the wiener index and edge-wiener index of power graph P(Zn), using m,n and Euler function. Also, we obtain an equivalence between the edge-wiener index and wiener index of a power graph of Zn.