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On the general sum-connectivity index of tricyclic graphs

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Abstract

The general sum-connectivity index of a graph G is a molecular descriptor defined as \(\chi _{\alpha }(G)=\sum _{uv\in E(G)}(d_G(u)+d_G(v))^\alpha \), where \(d_G(u)\) denotes the degree of vertex u in G and \(\alpha \) is a real number. In this paper, we obtain the first third graphs with maximum general sum-connectivity index among the connected tricyclic graphs of order n for \(\alpha \ge 1\) by four transformations which increase the general sum-connectivity index.

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Acknowledgments

The authors would like to express their sincere gratitude to the referees for a very careful reading of the paper and for all their insightful comments and valuable suggestions, which led to a number of improvements in this paper. This project is supported by Nature Science Foundation of Hubei Province (2014CFC1118), the foundation of State Ethnic Affairs Commission (14ZNZ023), the Special Fund for Basic Scientific Research of Central Colleges, South-Central University for Nationalities (CZW15084, CZW15063) and the Scientific Research Foundation of Graduate School of South Central University for Nationalities.

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  1. South Central University for Nationalities, Wuhan, 430074, People’s Republic of China

    Zhongxun Zhu & Hongyan Lu

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  1. Zhongxun Zhu
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  2. Hongyan Lu
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Correspondence to Zhongxun Zhu.

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Zhu, Z., Lu, H. On the general sum-connectivity index of tricyclic graphs. J. Appl. Math. Comput. 51, 177–188 (2016). https://doi.org/10.1007/s12190-015-0898-2

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