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Abstract
We give a formula for the number of spanning trees in a chain of cycles that have connected intersection of one edge but where the cycles have variable sizes. The formula uses basic properties of continued fractions.
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References
- BIER, T. 1995. Eine Charakterisierung zyklischer Polytope durch Kettenbrüche, Archiv der Mathematik 16: 545-554.
- BOGDANOWICZ, Z.R. 2008. Formulas for the number of spanning trees in a fan, Applied Mathematical Sciences 2: 781-786, Hikari Ltd.
- HASHIMOTO, K. 1989. Zeta Functions of finite graphs and representations of p-adic groups, Advanced Study in Pure Mathematics, vol 15, Academic Press NY pp. 211-280.
- IHARA, Y. 1966. On discrete Subgroups of the two by two projective linear group over p-adic fields, J. Math Soc Japan 18: 219-235.
- NORTHSHIELD, S. 1994. Several Proofs of Ihara's theorem, IMA preprint series No 1459.
- SEDLACEK, J. 1970. Lucas Numbers in Graph Theory, In Mathematics (Geometry and Graph Theory) Univ. Karlova, Prague p. 111-115.
- STARK, H. and TERRAS, A. 1995. Zeta functions of finite Graphs and Coverings, MSRI Preprint No 074-95.
References
BIER, T. 1995. Eine Charakterisierung zyklischer Polytope durch Kettenbrüche, Archiv der Mathematik 16: 545-554.
BOGDANOWICZ, Z.R. 2008. Formulas for the number of spanning trees in a fan, Applied Mathematical Sciences 2: 781-786, Hikari Ltd.
HASHIMOTO, K. 1989. Zeta Functions of finite graphs and representations of p-adic groups, Advanced Study in Pure Mathematics, vol 15, Academic Press NY pp. 211-280.
IHARA, Y. 1966. On discrete Subgroups of the two by two projective linear group over p-adic fields, J. Math Soc Japan 18: 219-235.
NORTHSHIELD, S. 1994. Several Proofs of Ihara's theorem, IMA preprint series No 1459.
SEDLACEK, J. 1970. Lucas Numbers in Graph Theory, In Mathematics (Geometry and Graph Theory) Univ. Karlova, Prague p. 111-115.
STARK, H. and TERRAS, A. 1995. Zeta functions of finite Graphs and Coverings, MSRI Preprint No 074-95.