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Chattopadhyay, S. and Panigrahi, P. (2017) On Sum of Powers of the Laplacian Eigenvalues of Power Graphs of Certain Finite Groups. Electronic Notes in Discrete Mathematics, 63, 137-143.

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• 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.