Ihara Zeta Function and Spectrum of the Cone Over a Semiregular Bipartite Graph

  • Deqiong Li
  • Yaoping HouEmail author
Original Paper


In this paper, a formula for the Ihara zeta function of the cone over a semiregular bipartite graph is derived. Using this formula, we show that two cones over semiregular bipartite graphs are cospectral if and only if they have the same Ihara zeta function. Moreover, the convergence of the zeta function of this family of graphs is considered.


Ihara zeta function Cone over semiregular bipartite graph Spectrum Pole Complexity 

Mathematics Subject Classification

05C50 15A15 



This work is supported by the National Natural Science Foundation of China (No. 11571101) and the Natural Science Foundation of Hunan Province, China (Grant 2019JJ40184, 2019JJ50173). The authors would like to thank the anonymous referees for their valuable comments and careful reviewing of this paper. In particular, the suggestion on the simplication and improvement for the proof of Theorem 6 is gratefully acknowledged.


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Copyright information

© Springer Japan KK, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Key Laboratory of High Performance Computing and Stochastic Information Processing, College of Mathematics and StatisticsHunan Normal UniversityChangshaChina
  2. 2.College of Mathematics and ComputationHunan University of Science and TechnologyXiangtanChina

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