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On the Additively Weighted Harary Index of Some Composite Graphs

Author

Listed:
  • Behrooz Khosravi

    (Department of Pure Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), 424, Hafez Ave., Tehran 15914, Iran)

  • Elnaz Ramezani

    (Department of Pure Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), 424, Hafez Ave., Tehran 15914, Iran)

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 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.

Suggested Citation

  • Behrooz Khosravi & Elnaz Ramezani, 2017. "On the Additively Weighted Harary Index of Some Composite Graphs," Mathematics, MDPI, vol. 5(1), pages 1-13, March.
    • Handle: RePEc:gam:jmathe:v:5:y:2017:i:1:p:16-:d:92317
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