On the Harary index of graph operations

Kinkar C. Das; Kexiang Xu; Ismail Naci Cangul; Ahmet Sinan Cevik; Ante Graovac

doi:10.1186/1029-242X-2013-339

On the Harary index of graph operations

Kinkar C. Das
, Kexiang Xu
, Ismail Naci Cangul
, Ahmet Sinan Cevik
, Ante Graovac

Department of Mathematics

Nanjing University of Aeronautics and Astronautics
Uludag University
Selcuk University
University of Split

Research output: Contribution to journal › Article › peer-review

42 Scopus citations

Abstract

The Harary index is defined as the sum of reciprocals of distances between all pairs of vertices of a connected graph. In this paper, expressions for the Harary indices of the join, corona product, Cartesian product, composition and disjunction of graphs are derived and the indices for some well-known graphs are evaluated. In derivations some terms appear which are similar to the Harary index and we name them the second and third Harary index.

Original language	English
Article number	339
Journal	Journal of Inequalities and Applications
Volume	2013
DOIs	https://doi.org/10.1186/1029-242X-2013-339
State	Published - Dec 2013

Keywords

Graph
Graph operations
Harary index

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10.1186/1029-242X-2013-339

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title = "On the Harary index of graph operations",

abstract = "The Harary index is defined as the sum of reciprocals of distances between all pairs of vertices of a connected graph. In this paper, expressions for the Harary indices of the join, corona product, Cartesian product, composition and disjunction of graphs are derived and the indices for some well-known graphs are evaluated. In derivations some terms appear which are similar to the Harary index and we name them the second and third Harary index.",

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AB - The Harary index is defined as the sum of reciprocals of distances between all pairs of vertices of a connected graph. In this paper, expressions for the Harary indices of the join, corona product, Cartesian product, composition and disjunction of graphs are derived and the indices for some well-known graphs are evaluated. In derivations some terms appear which are similar to the Harary index and we name them the second and third Harary index.

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KW - Harary index

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On the Harary index of graph operations

Abstract

Keywords

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