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Bartholdi Zeta Functions of Generalized Join Graphs

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Abstract

Let \(G=H[G_1,G_2,\ldots ,G_k]\) be the generalized join graph of\(G_1,G_2,\ldots ,G_k\) determined by H. In this paper, we give a decomposition formula for the Bartholdi zeta function of G. As applications, we obtain explicit formulae for Bartholdi zeta functions of some special kinds of graphs, such as the complete multipartite graph, the wheel, etc.

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Acknowledgements

We are grateful to the anonymous referees for their careful reading and valuable suggestions. These suggestions help us to improve the presentation of the paper dramatically.

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Authors and Affiliations

  1. School of Sciences, Jimei University, Xiamen, 361021, Fujian, People’s Republic of China

    Haiyan Chen & Yu Chen

Authors
  1. Haiyan Chen
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  2. Yu Chen
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Corresponding author

Correspondence to Haiyan Chen.

Additional information

This work is supported by the National Natural Science Foundation of China (Grant 11771181, 11171134) and the Natural Science Foundation of Fujian Province,China (Grant 2015J01017, 2013J01014).

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Chen, H., Chen, Y. Bartholdi Zeta Functions of Generalized Join Graphs. Graphs and Combinatorics 34, 207–222 (2018). https://doi.org/10.1007/s00373-017-1867-3

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  • DOI: https://doi.org/10.1007/s00373-017-1867-3

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