Korean Journal of Mathematics

  • 제26권4호
  • /
  • Pages.741-746
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  • 2018
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  • 1976-8605(pISSN)
  • /
  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
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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)
  • 투고 : 2018.10.29
  • 심사 : 2018.12.13
  • 발행 : 2018.12.30
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초록

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.

키워드

E1KKMK_2018_v26n4_741_f0001.png 이미지

FIGURE 1. Dumbbell graph Da,b,n

E1KKMK_2018_v26n4_741_f0002.png 이미지

FIGURE 2. Dumbbell graph D1,1,n

E1KKMK_2018_v26n4_741_f0003.png 이미지

FIGURE 3. Dumbbell graph D1,2,n

참고문헌

  1. H. Bass, The Ihara-Selberg zeta function of a tree lattice, International. J. Math. 3 (1992), 717-797. https://doi.org/10.1142/S0129167X92000357
  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. https://doi.org/10.2969/jmsj/01830219
  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

피인용 문헌

  1. IHARA ZETA FUNCTION OF FINITE GRAPHS WITH CIRCUIT RANK TWO vol.28, pp.1, 2018, https://doi.org/10.11568/kjm.2020.28.1.123