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Journal of Chemistry
Volume 2017 (2017), Article ID 3531746, 7 pages
https://doi.org/10.1155/2017/3531746
Research Article

On the Resistance-Harary Index of Graphs Given Cut Edges

Huaiyin Institute of Technology, Faculty of Mathematics and Physics, Huai’an, Jiangsu 223003, China

Correspondence should be addressed to Hongzhuan Wang

Received 22 June 2017; Accepted 26 November 2017; Published 21 December 2017

Academic Editor: Robert Zaleśny

Copyright © 2017 Hongzhuan Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Graphs are often used to describe the structure of compounds and drugs. Each vertex in the graph represents the molecule and each edge represents the bond between the atoms. The resistance distance between any two vertices is equal to the resistance between the two points of an electrical network. The Resistance-Harary index is defined as the sum of reciprocals of resistance distances between all pairs of vertices. In this paper, the extremal graphs with maximum Resistance-Harary index are determined in connected graphs with given vertices and cut edges.