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The Ihara zeta function of the complement of a semiregular bipartite graph |
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| Institution: | 1. College of Science, Hunan University of Technology and Business, Changsha, Hunan 410205, China;2. Key Laboratory of Hunan Province for Statistical Learning and Intelligent Computation, Hunan University of Technology and Business, Changsha, Hunan 410205, China;3. College of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, China;4. School of Science, Zhejiang University of Science and Technology, Hangzhou, Zhejiang, 310023, China |
| Abstract: | We study the Ihara zeta function of the complement of a semiregular bipartite graph. A factorization formula for the Ihara zeta function is derived via which the number of spanning trees is computed. For a class of complements of semiregular bipartite graphs, it is shown that they have the same Ihara zeta function if and only if they are cospectral. |
| Keywords: | Ihara zeta function Spectrum Semiregular bipartite graph Complement |
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