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Keywords = additively weighted harary index

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13 pages, 404 KiB  
Article
On the Additively Weighted Harary Index of Some Composite Graphs
by Behrooz Khosravi and Elnaz Ramezani
Mathematics 2017, 5(1), 16; https://doi.org/10.3390/math5010016 - 7 Mar 2017
Cited by 5 | Viewed by 3430
Abstract
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 [...] Read more.
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. Full article
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