Ihara Zeta Function and Spectrum of the Cone Over a Semiregular Bipartite Graph
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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.
KeywordsIhara zeta function Cone over semiregular bipartite graph Spectrum Pole Complexity
Mathematics Subject Classification05C50 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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