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The Wiener Index of r-Uniform Hypergraphs

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Abstract

The Wiener index of a hypergraph is the sum of distances between all pairs of vertices of the hypergraph. In this paper, we first investigate the Wiener index of some special r-uniform paths and r-uniform cycles. The Wiener index of different kinds of 3-uniform paths were also considered. Then we explore the lower bound of Wiener index in a r-uniform hypergraph on n vertices with a given circumference which is the maximum length of a cycle in a hypergraph. In the last part, we propose the concept of the chemical bond-Wiener index of a graph, which is the sum of the distances between all pairs of chemical bonds of a graph, considering the removing of hydrogen atoms. The polyphenyl chains with minimum and maximum chemical bond-Wiener indices among all the polyphenyl chains with h hexagons were completely determined.

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Acknowledgments

The authors feel greatly indebted to the anonymous referees for their careful reading and accurate suggestions on improving the presentation. The authors were supported by grants NSFC (11271006), the Scientific Research Program (XJEDU2014I046) of Higher Education Institution of XinJiang Uygur Autonomous Region, and the Scientific Research Program (201442137-03) of XinJiang Uygur Autonomous Region.

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Authors and Affiliations

  1. School of Mathematics, Shandong University, Jinan, 250100, People’s Republic of China

    Lin Sun, Jianliang Wu, Hua Cai & Zhaoyang Luo

  2. Department of Mathematics, Changji College, Changji, 831100, People’s Republic of China

    Lin Sun, Hua Cai & Zhaoyang Luo

Authors
  1. Lin Sun
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  2. Jianliang Wu
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  3. Hua Cai
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  4. Zhaoyang Luo
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Corresponding author

Correspondence to Jianliang Wu.

Additional information

Communicated by Ang Miin Huey.

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Sun, L., Wu, J., Cai, H. et al. The Wiener Index of r-Uniform Hypergraphs. Bull. Malays. Math. Sci. Soc. 40, 1093–1113 (2017). https://doi.org/10.1007/s40840-016-0359-6

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  • DOI: https://doi.org/10.1007/s40840-016-0359-6

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