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Mathematics 2017, 5(1), 16; doi:10.3390/math5010016

On the Additively Weighted Harary Index of Some Composite Graphs

Department of Pure Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), 424, Hafez Ave., Tehran 15914, Iran
Author to whom correspondence should be addressed.
Academic Editor: Michael Falk
Received: 3 November 2016 / Revised: 2 February 2017 / Accepted: 21 February 2017 / Published: 7 March 2017
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The Harary index is defined as the sum of reciprocals of distances between all pairs of vertices of a connected graph. The additively weighted Harary index H A ( G ) is a modification of the Harary index in which the contributions of vertex pairs are weighted by the sum of their degrees. This new invariant was introduced in (Alizadeh, Iranmanesh and Došlić. Additively weighted Harary index of some composite graphs, Discrete Math, 2013) and they posed the following question: What is the behavior of H A ( G ) when G is a composite graph resulting for example by: splice, link, corona and rooted product? We investigate the additively weighted Harary index for these standard graph products. Then we obtain lower and upper bounds for some of them. View Full-Text
Keywords: additively weighted harary index; composite graph; corona; rooted product; splice; link additively weighted harary index; composite graph; corona; rooted product; splice; link

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. (CC BY 4.0).

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Khosravi, B.; Ramezani, E. On the Additively Weighted Harary Index of Some Composite Graphs. Mathematics 2017, 5, 16.

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