Bounds on Harary index

Kinkar Ch Das; Bo Zhou; N. Trinajstić

doi:10.1007/s10910-009-9522-8

Bounds on Harary index

Kinkar Ch Das
, Bo Zhou
, N. Trinajstić

Department of Mathematics

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

56 Scopus citations

Abstract

In this paper, we obtain the lower and upper bounds on the Harary index of a connected graph (molecular graph), and, in particular, of a triangle- and quadrangle-free graphs in terms of the number of vertices, the number of edges and the diameter. We give the Nordhaus-Gaddum-type result for Harary index using the diameters of the graph and its complement. Moreover, we compare Harary index and reciprocal complementary Wiener number for graphs.

Original language	English
Pages (from-to)	1377-1393
Number of pages	17
Journal	Journal of Mathematical Chemistry
Volume	46
Issue number	4
DOIs	https://doi.org/10.1007/s10910-009-9522-8
State	Published - Oct 2009

Keywords

Diameter
Harary index
Lower bound
Quadrangle-free graphs
Triangle-free graphs
Upper bound

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10.1007/s10910-009-9522-8

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abstract = "In this paper, we obtain the lower and upper bounds on the Harary index of a connected graph (molecular graph), and, in particular, of a triangle- and quadrangle-free graphs in terms of the number of vertices, the number of edges and the diameter. We give the Nordhaus-Gaddum-type result for Harary index using the diameters of the graph and its complement. Moreover, we compare Harary index and reciprocal complementary Wiener number for graphs.",

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AB - In this paper, we obtain the lower and upper bounds on the Harary index of a connected graph (molecular graph), and, in particular, of a triangle- and quadrangle-free graphs in terms of the number of vertices, the number of edges and the diameter. We give the Nordhaus-Gaddum-type result for Harary index using the diameters of the graph and its complement. Moreover, we compare Harary index and reciprocal complementary Wiener number for graphs.

KW - Diameter

KW - Harary index

KW - Lower bound

KW - Quadrangle-free graphs

KW - Triangle-free graphs

KW - Upper bound

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JF - Journal of Mathematical Chemistry

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Bounds on Harary index

Abstract

Keywords

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