Korean J. Math.  Vol 28, No 1 (2020)  pp.123-136
DOI: https://doi.org/10.11568/kjm.2020.28.1.123

Ihara zeta function of finite graphs with circuit rank two

Sanghoon Kwon, Seungmin Lee

Abstract


In this paper, we give an explicit formula as a rational function for the Ihara zeta function of every finite connected graph without degree one vertices whose circuit rank is two.

Keywords


Ihara zeta function, circuit rank, matrix analysis

Subject classification

05C50, 15A24, 37C30

Sponsor(s)

Catholic Kwandong University

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References


H. Bass, The Ihara-Selberg zeta function of a tree lattice, Int. J. Math. 3 (1992) 717–797 (Google Scholar)

Y. Ihara, On discrete subgroups of the two by two projective linear group over p-adic fields, J. Math. Soc. Japan 18 (1966), 219–235. (Google Scholar)

N. Konno, H. Mitsuhashi, H. Morita and I. Sato, A new weighted Ihara zeta function for a graph, Linear Algebra and its Applications. 571 (2019) 154–179. (Google Scholar)

S. Kwon and J. Park, Ihara zeta function of dumbbell graphs, Korean J. Math. 26 (2018) 741–746. (Google Scholar)

M. Kotani and T. Sunada, Zeta functions of finite graphs, J. Math. Sci. Univ. Tokyo, 7 (2000), 7–25 (Google Scholar)

A. Selberg, Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series, J. Indian Math. Soc. (N.S.) 20 (1956), 47–87 (Google Scholar)

J.-P. Serre, Trees, Springer Monographs in Mathematics (2003) (Google Scholar)

A. Terras, Zeta function of graphs: A Stroll through the Garden, Cambridge Studies in Advanced Mathematics. 128 (2010) (Google Scholar)


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