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The coefficients
of the Ihara zeta function
Geoffrey Scott and Christopher Storm
Vol. 1 (2008), No. 2, 217–233
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Abstract |
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In her Ph.D. Thesis, Czarneski began a preliminary study of the coefficients of the reciprocal of the Ihara zeta function of a finite graph. We give a survey of the results in this area and then give a complete characterization of the coefficients. As an application, we give a (very poor) bound on the number of Eulerian circuits in a graph. We also use these ideas to compute the zeta function of graphs which are cycles with a single chord. We conclude by posing several questions for future work. |
Keywords
Ihara zeta, polynomial coefficient, graph zeta, Eulerian
circuit, graph, digraph, oriented line graph
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Mathematical Subject Classification 2000
Primary: 00A05
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Milestones
Received: 29 October 2007
Revised: 28 February 2008
Accepted: 6 May 2008
Published: 1 July 2008
Communicated by Andrew Granville
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Authors |
| Geoffrey Scott | |
| Department of Mathematics 2074 East Hall 530 Church Street Ann Arbor, MI 48109-1043 United States |
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| Christopher Storm | |
| Department of Mathematics and
Computer Science 111 Alumnae Hall Adelphi University Garden City, NY 11530 United States |
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| http://www.adelphi.edu/~stormc | |
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