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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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참고문헌 (5)
참고문헌 신청
H. Bass / 1992 / The Ihara-Selberg zeta function of a tree lattice / International. J. Math. 3 :717~797
M. D. Horton / 2006 / What are zeta functions of graphs and what are they good for ? / Contemporary Mathematics 415:173~190
Y. Ihara / 1966 / On discrete subgroups of the two by two projective linear group over p-adic fields / J. Math. Soc. Japan 18:219~235
M. Kotani / 2000 / Zeta function of finite graphs / J. Math. Sci. Univ. Tokyo 7:7~25
A. Terras / 2011 / CambridgeX Studies in Advanced Mathematics, Vol. 128 / Cambridge University Press :239
M. D. Horton / 2006 / What are zeta functions of graphs and what are they good for ? / Contemporary Mathematics 415:173~190
Y. Ihara / 1966 / On discrete subgroups of the two by two projective linear group over p-adic fields / J. Math. Soc. Japan 18:219~235
M. Kotani / 2000 / Zeta function of finite graphs / J. Math. Sci. Univ. Tokyo 7:7~25
A. Terras / 2011 / CambridgeX Studies in Advanced Mathematics, Vol. 128 / Cambridge University Press :239
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