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The Minimum General Sum-Connectivity Index of Trees with Given Matching Number

  • Lingping ZhongEmail author
  • Qiuping Qian
Article
  • 12 Downloads

Abstract

The general sum-connectivity index of a graph G is defined as \(\chi _\alpha (G)=\sum _{uv\in E(G)}(d(u)+d(v))^{\alpha }\), where d(u) denotes the degree of a vertex u in G and \(\alpha \) is a real number. In this paper, we determine the minimum general sum-connectivity indices of trees with n vertices and matching number m, where \(n=2m\) for \(\alpha \le -\,2\) and \(2m\le n\le 3m+1\) for \(\alpha >1\), respectively. The corresponding extremal graphs are also characterized.

Keywords

Randić index General sum-connectivity index Sum-connectivity index Tree Matching number 

Mathematics Subject Classification

05C05 05C07 05C35 92E10 

Notes

Acknowledgements

The authors would like to thank the anonymous referees for their helpful comments and suggestions which improved the presentation of the paper. This work was supported by the National Natural Science Foundation of China (No. 11501291) and the Fundamental Research Funds for the Central Universities (No. NS2015078).

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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2019

Authors and Affiliations

  1. 1.Department of MathematicsNanjing University of Aeronautics and AstronauticsNanjingPeople’s Republic of China

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