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Volumn 1, Issue 2, 2008, Pages 217-233

The coefficients of the Ihara zeta function

Author keywords

digraph; Eulerian circuit; graph; graph zeta; Ihara zeta; oriented line graph; polynomial coefficient

Indexed keywords


EID: 58349092257     PISSN: 19444176     EISSN: 19444184     Source Type: Journal    
DOI: 10.2140/involve.2008.1.217     Document Type: Article
Times cited : (23)

References (25)
  • 1
    • 0000387327 scopus 로고
    • The Ihara–Selberg zeta function of a tree lattice
    • [Bass 1992] MR 94a:11072 Zbl 0767.11025
    • [Bass 1992] H. Bass, “The Ihara–Selberg zeta function of a tree lattice”, Internat. J. Math. 3:6 (1992), 717–797. MR 94a:11072 Zbl 0767.11025
    • (1992) Internat. J. Math , vol.3 , Issue.6 , pp. 717-797
    • Bass, H.1
  • 2
    • 0004242420 scopus 로고
    • [Biggs 1994] 2nd ed., Cambridge University Press, Cambridge, MR 95h:05105 Zbl 0797.05032
    • [Biggs 1994] N. Biggs, Algebraic graph theory, 2nd ed., Cambridge University Press, Cambridge, 1994. MR 95h:05105 Zbl 0797.05032
    • (1994) Algebraic graph theory
    • Biggs, N.1
  • 4
    • 0004275036 scopus 로고
    • [Chartrand and Lesniak 1986] 2nd ed., Wads-worth–Brooks/Cole, Monterey, CA, MR 87h:05001 Zbl 0666.05001
    • [Chartrand and Lesniak 1986] G. Chartrand and L. Lesniak, Graphs and digraphs, 2nd ed., Wads-worth–Brooks/Cole, Monterey, CA, 1986. MR 87h:05001 Zbl 0666.05001
    • (1986) Graphs and digraphs
    • Chartrand, G.1    Lesniak, L.2
  • 6
    • 68349084926 scopus 로고    scopus 로고
    • [Czarneski 2005] Ph.D. thesis, Louisiana State Univ., Baton Rouge
    • [Czarneski 2005] D. L. Czarneski, Zeta functions of finite graphs, Ph.D. thesis, Louisiana State Univ., Baton Rouge, 2005.
    • (2005) Zeta functions of finite graphs
    • Czarneski, D. L.1
  • 7
    • 0001080062 scopus 로고
    • The determinant of the adjacency matrix of a graph
    • [Harary 1962] MR 26 #1876 Zbl 0113.17406
    • [Harary 1962] F. Harary, “The determinant of the adjacency matrix of a graph”, SIAM Rev. 4 (1962), 202–210. MR 26 #1876 Zbl 0113.17406
    • (1962) SIAM Rev , vol.4 , pp. 202-210
    • Harary, F.1
  • 8
    • 0348104610 scopus 로고
    • Determinants, permanents and bipartite graphs
    • [Harary 1969a] MR 39 #4035 Zbl 0273.15006
    • [Harary 1969a] F. Harary, “Determinants, permanents and bipartite graphs”, Math. Mag. 42 (1969), 146–148. MR 39 #4035 Zbl 0273.15006
    • (1969) Math. Mag , vol.42 , pp. 146-148
    • Harary, F.1
  • 9
    • 0003780715 scopus 로고
    • [Harary 1969b] Addison-Wesley, Reading, MA, MR 41 #1566 Zbl 0182.57702
    • [Harary 1969b] F. Harary, Graph theory, Addison-Wesley, Reading, MA, 1969. MR 41 #1566 Zbl 0182.57702
    • (1969) Graph theory
    • Harary, F.1
  • 11
    • 34547679564 scopus 로고    scopus 로고
    • What are zeta functions of graphs and what are they good for?
    • [Horton et al. 2006] in (Snowbird, UT, 2005), edited by G. Berkolaiko et al., Contemp. Math. 415, Amer. Math. Soc., Providence, RI, 2006. MR 2007i:05088 Zbl 05082575
    • [Horton et al. 2006] M. D. Horton, H. M. Stark, and A. A. Terras, “What are zeta functions of graphs and what are they good for?”, pp. 173–189 in Quantum graphs and their applications (Snowbird, UT, 2005), edited by G. Berkolaiko et al., Contemp. Math. 415, Amer. Math. Soc., Providence, RI, 2006. MR 2007i:05088 Zbl 05082575
    • Quantum graphs and their applications , pp. 173-189
    • Horton, M. D.1    Stark, H. M.2    Terras, A. A.3
  • 12
    • 0001273782 scopus 로고    scopus 로고
    • ℘)
    • [Ihara 1966a] in (Boulder, CO, 1965), Amer. Math. Soc., Providence, R.I., 1966. MR 34 #5777 Zbl 0261.20029
    • ℘)”, pp. 272–278 in Algebraic groups and discontinuous subgroups (Boulder, CO, 1965), Amer. Math. Soc., Providence, R.I., 1966. MR 34 #5777 Zbl 0261.20029
    • Algebraic groups and discontinuous subgroups , pp. 272-278
    • Ihara, Y.1
  • 13
    • 84972492382 scopus 로고
    • On discrete subgroups of the two by two projective linear group over p-adic fields
    • [Ihara 1966b] MR 36 #6511 Zbl 0158.27702
    • [Ihara 1966b] 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. MR 36 #6511 Zbl 0158.27702
    • (1966) J. Math. Soc. Japan , vol.18 , pp. 219-235
    • Ihara, Y.1
  • 14
    • 4243139497 scopus 로고    scopus 로고
    • A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries
    • [Jerrum et al. 2004] MR 2006b:15013
    • [Jerrum et al. 2004] M. Jerrum, A. Sinclair, and E. Vigoda, “A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries”, J. ACM 51:4 (2004), 671–697. MR 2006b:15013
    • (2004) J. ACM , vol.51 , Issue.4 , pp. 671-697
    • Jerrum, M.1    Sinclair, A.2    Vigoda, E.3
  • 15
    • 0002286175 scopus 로고    scopus 로고
    • Zeta functions of finite graphs
    • [Kotani and Sunada 2000] MR 2001f:68110 Zbl 0978.05051
    • [Kotani and Sunada 2000] M. Kotani and T. Sunada, “Zeta functions of finite graphs”, J. Math. Sci. Univ. Tokyo 7:1 (2000), 7–25. MR 2001f:68110 Zbl 0978.05051
    • (2000) J. Math. Sci. Univ. Tokyo , vol.7 , Issue.1 , pp. 7-25
    • Kotani, M.1    Sunada, T.2
  • 17
    • 2142838434 scopus 로고    scopus 로고
    • On graphs determined by their Tutte polynomi-als
    • [de Mier and Noy 2004] MR 2005a:05057 Zbl 1053.05057
    • [de Mier and Noy 2004] A. de Mier and M. Noy, “On graphs determined by their Tutte polynomi-als”, Graphs Combin. 20:1 (2004), 105–119. MR 2005a:05057 Zbl 1053.05057
    • (2004) Graphs Combin , vol.20 , Issue.1 , pp. 105-119
    • de Mier, A.1    Noy, M.2
  • 18
    • 33746404807 scopus 로고    scopus 로고
    • Ramanujan graphs
    • [Murty 2003] MR 2004d:11092 Zbl 1038.05038
    • [Murty 2003] M. R. Murty, “Ramanujan graphs”, J. Ramanujan Math. Soc. 18:1 (2003), 33–52. MR 2004d:11092 Zbl 1038.05038
    • (2003) J. Ramanujan Math. Soc , vol.18 , Issue.1 , pp. 33-52
    • Murty, M. R.1
  • 19
    • 0141525079 scopus 로고    scopus 로고
    • Graphs determined by polynomial invariants
    • [Noy 2003] MR 2004k:05169 Zbl 1048.05072
    • [Noy 2003] M. Noy, “Graphs determined by polynomial invariants”, Theoret. Comput. Sci. 307:2 (2003), 365–384. MR 2004k:05169 Zbl 1048.05072
    • (2003) Theoret. Comput. Sci , vol.307 , Issue.2 , pp. 365-384
    • Noy, M.1
  • 20
    • 0030585874 scopus 로고    scopus 로고
    • Zeta functions of finite graphs and cover-ings
    • [Stark and Terras 1996] MR 98b:11094 Zbl 0874.11064
    • [Stark and Terras 1996] H. M. Stark and A. A. Terras, “Zeta functions of finite graphs and cover-ings”, Adv. Math. 121:1 (1996), 124–165. MR 98b:11094 Zbl 0874.11064
    • (1996) Adv. Math , vol.121 , Issue.1 , pp. 124-165
    • Stark, H. M.1    Terras, A. A.2
  • 21
    • 0034259232 scopus 로고    scopus 로고
    • Zeta functions of finite graphs and coverings, II
    • [Stark and Terras 2000] MR 2002f:11123 Zbl 0972.11086
    • [Stark and Terras 2000] H. M. Stark and A. A. Terras, “Zeta functions of finite graphs and coverings, II”, Adv. Math. 154:1 (2000), 132–195. MR 2002f:11123 Zbl 0972.11086
    • (2000) Adv. Math , vol.154 , Issue.1 , pp. 132-195
    • Stark, H. M.1    Terras, A. A.2
  • 22
    • 85059142331 scopus 로고    scopus 로고
    • [Stein 2008]
    • [Stein 2008] W. Stein, SAGE reference manual, 2008, Available at http://www.sagemath.org/doc/html/ref/index.html.
    • (2008) SAGE reference manual
    • Stein, W.1
  • 24
    • 33750438827 scopus 로고    scopus 로고
    • Zeta functions of finite graphs and coverings, III
    • [Terras and Stark 2007] MR 2304325 Zbl 05078979
    • [Terras and Stark 2007] A. A. Terras and H. M. Stark, “Zeta functions of finite graphs and coverings, III”, Adv. Math. 208:1 (2007), 467–489. MR 2304325 Zbl 05078979
    • (2007) Adv. Math , vol.208 , Issue.1 , pp. 467-489
    • Terras, A. A.1    Stark, H. M.2
  • 25
    • 49249151236 scopus 로고
    • The complexity of computing the permanent
    • [Valiant 1979] MR 80f:68054 Zbl 0415.68008
    • [Valiant 1979] L. G. Valiant, “The complexity of computing the permanent”, Theoret. Comput. Sci. 8:2 (1979), 189–201. MR 80f:68054 Zbl 0415.68008
    • (1979) Theoret. Comput. Sci , vol.8 , Issue.2 , pp. 189-201
    • Valiant, L. G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.