DOI QR코드

DOI QR Code

IHARA ZETA FUNCTION OF FINITE GRAPHS WITH CIRCUIT RANK TWO

  • Kwon, Sanghoon (Department of Mathematical Education Catholic Kwandong University) ;
  • Lee, Seungmin (Department of Mathematical Education Catholic Kwandong University)
  • 투고 : 2019.09.18
  • 심사 : 2020.03.16
  • 발행 : 2020.03.30

초록

In this paper, we give an explicit formula as a rational function for the Ihara zeta function of every finite connected graph without degree one vertices whose circuit rank is two.

키워드

참고문헌

  1. H. Bass, The Ihara-Selberg zeta function of a tree lattice, Int. J. Math. 3 (1992) 717-797 https://doi.org/10.1142/S0129167X92000357
  2. 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
  3. N. Konno, H. Mitsuhashi, H. Morita and I. Sato, A new weighted Ihara zeta function for a graph, Linear Algebra and its Applications. 571 (2019) 154-179. https://doi.org/10.1016/j.laa.2019.02.022
  4. S. Kwon and J. Park, Ihara zeta function of dumbbell graphs, Korean J. Math. 26 (2018) 741-746. https://doi.org/10.11568/KJM.2018.26.4.741
  5. M. Kotani and T. Sunada, Zeta functions of finite graphs, J. Math. Sci. Univ. Tokyo, 7 (2000), 7-25
  6. A. Selberg, Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series, J. Indian Math. Soc. (N.S.) 20 (1956), 47-87
  7. J.-P. Serre, Trees, Springer Monographs in Mathematics (2003)
  8. A. Terras, Zeta function of graphs: A Stroll through the Garden, Cambridge Studies in Advanced Mathematics. 128 (2010)