[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.11568/kjm.2018.26.4.741

IHARA ZETA FUNCTION OF DUMBBELL GRAPHS

Kwon, Sanghoon (Department of Mathematical Education, Catholic Kwandong University)
Park, Jung-Hyeon (Department of Mathematical Education, Catholic Kwandong University)

Publication Information

Korean Journal of Mathematics / v.26, no.4, 2018 , pp. 741-746 More about this Journal

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.

Keywords

Ihara zeta function; dumbbell graphs; prime geodesic theorem;

Citations & Related Records

Reference

1	H. Bass, The Ihara-Selberg zeta function of a tree lattice, International. J. Math. 3 (1992), 717-797. DOI
2	M. D. Horton, H. M. Stark, and A. Terras, What are zeta functions of graphs and what are they good for ?, Contemporary Mathematics 415 (2006), Quantum Graphs and Their Applications; Edited by Gregory Berkolaiko, Robert Carlson, Stephen A. Fulling, and Peter Kuchment, 173-190.
3	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. DOI
4	M. Kotani and T. Sunada, Zeta function of finite graphs, J. Math. Sci. Univ. Tokyo 7 (2000), 7-25.
5	A. Terras, Zeta functions of graphs: a stroll through the garden, CambridgeX Studies in Advanced Mathematics, Vol. 128, Cambridge University Press, Cambridge, 2011, xii+239 pp