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

Sanghoon Kwon, Jung-Hyeon Park


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.


Ihara zeta function, dumbbell graphs, prime geodesic theorem

Subject classification

28A33; 37C85; 22E40


Catholic Kwandong University

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