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
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
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 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.
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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MDPI and ACS Style
Khosravi, B.; Ramezani, E. On the Additively Weighted Harary Index of Some Composite Graphs. Mathematics 2017, 5, 16.
Khosravi B, Ramezani E. On the Additively Weighted Harary Index of Some Composite Graphs. Mathematics. 2017; 5(1):16.
Khosravi, Behrooz; Ramezani, Elnaz. 2017. "On the Additively Weighted Harary Index of Some Composite Graphs." Mathematics 5, no. 1: 16.
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