The Wiener Index of an Undirected Power Graph

作     者：Volkan Aşkin Şerife Büyükköse Volkan Aşkin;Şerife Büyükköse

作者机构：Gazi University Mathematics Ankara Turkey 

出 版 物：《Advances in Linear Algebra & Matrix Theory》 (线性代数与矩阵理论研究进展（英文）)

年 卷 期：2021年第11卷第1期

页      面：21-29页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Wiener Index Edge-Wiener Index An Undirected Power Graph Line Graph 

摘      要：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.