Korean J. Math. Vol. 26 No. 4 (2018) pp.741-746
DOI: https://doi.org/10.11568/kjm.2018.26.4.741

Ihara zeta function of dumbbell graphs

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Published: Dec 17, 2018
Keywords:
Ihara zeta function, dumbbell graphs, prime geodesic theorem
Mathematics Subject Classification:
28A33, 37C85, 22E40

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Sanghoon Kwon
Department of Mathematical Education Catholic Kwandong University Gangneung, Korea
Jung-Hyeon Park
Department of Mathematical Education Catholic Kwandong University Gangneung, Korea

Abstract

We study the Ihara zeta function of the dumbbell graph $D_{1,1,n}$ of type $(1,1,n)$ and $D_{1,2,n}$ of type $(1,2,n)$. Explicit formulas of the zeta functions of the graphs, their radius of convergence, and the connection with the number of closed cycles are given.


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Supporting Agencies

Catholic Kwandong University

References

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