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On the Ihara Zeta Function of Cones Over Regular Graphs

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Abstract

In this paper we derive a formula of the Ihara zeta function of a cone over a regular graph that involves the spectrum of the adjacency matrix of the cone. We show that the Ihara zeta function and the spectrum of the adjacency matrix of the cone determine each other and we characterize those cones that satisfy the graph theory Riemann hypothesis.

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Authors and Affiliations

  1. Department of Mathematics, University of Northern Iowa, Cedar Falls, IA, 50614, USA

    Paymun Bayati & Marius Somodi

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  1. Paymun Bayati
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  2. Marius Somodi
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Correspondence to Marius Somodi.

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Bayati, P., Somodi, M. On the Ihara Zeta Function of Cones Over Regular Graphs. Graphs and Combinatorics 29, 1633–1646 (2013). https://doi.org/10.1007/s00373-012-1223-6

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  • DOI: https://doi.org/10.1007/s00373-012-1223-6

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