Further Results on Harmonic Index and Some New Relations Between Harmonic Index and Other Topological Indices

Volume 11, Issue 2, pp 123 - 136 http://dx.doi.org/10.22436/jmcs.011.02.05

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Authors

Khosro Sayehvand - Faculty of Mathematical Sciences, University of Malayer, P. O. Box 16846-13114, Malayer, Iran. Mohammadreza Rostami - Faculty of Mathematical Sciences, University of Malayer, P. O. Box 16846-13114, Malayer, Iran.

Abstract

The harmonic index \(H(G)\) of a graph \(G\) is defined as the sum of the weights \(\frac{2}{d_u+d_v}\) of all edges \(uv\) of \(G\) , where \(d_u\) denotes the degree of a vertex \(u\) in \(G\) . In this paper, we obtained some new relationships between harmonic index and first geometric-arithmetic index, sum connectivity index that this indices are important than another topological index. In addition, we determine the lower and upper bond for molecular graphs and unicyclic molecular graph. Also we give a characterization of the minimum harmonic index of graphs with maximum degree \(\Delta\).

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Keywords

• harmonic index
• first geometric-arithmetic index
• sum connectivity index
• molecular graph
• minimum degree
• maximum degree.

MSC

•  05C07
•  05C35
•  05C12
•  05C40

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