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The Wiener index of the th power of a graph

✍ Scribed by Xinhui An; Baoyindureng Wu

Publisher: Elsevier Science
Year: 2008
Tongue: English
Weight: 289 KB
Volume: 21
Category: Article
ISSN: 0893-9659
DOI: 10.1016/j.aml.2007.03.025

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✦ Synopsis

The kth power of a graph G, denoted by G k , is a graph with the same vertex set as G such that two vertices are adjacent in G k if and only if their distance is at most k in G. The Wiener index is a distance-based topological index defined as the sum of distances between all pairs of vertices in a graph. In this note, we give the bounds on the Wiener index of the graph G k . The Nordhaus-Gaddum-type inequality for the Wiener index of the graph G k is also presented.

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