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On the Zeros of Some Genus Polynomials

Published online by Cambridge University Press:  20 November 2018

Saul Stahl
Saul Stahl*
Affiliation:
Department of Mathematics, University of Kansas, Lawrence, KS, U.S.A. 66045 e-mail: [email protected]
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Abstract

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In the genus polynomial of the graph G, the coefficient of xk is the number of distinct embeddings of the graph G on the oriented surface of genus k. It is shown that for several infinite families of graphs all the zeros of the genus polynomial are real and negative. This implies that their coefficients, which constitute the genus distribution of the graph, are log concave and therefore also unimodal. The geometric distribution of the zeros of some of these polynomials is also investigated and some new genus polynomials are presented.

Keywords

05C1005A1530C1526C10
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 49 , Issue 3 , 01 June 1997 , pp. 617 - 640
Copyright
Copyright © Canadian Mathematical Society 1997

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