1 research outputs found
Log-concavity of the genus polynomials of Ringel ladders
A Ringel ladder can be formed by a self-bar-amalgamation operation on a
symmetric ladder, that is, by joining the root vertices on its end-rungs. The
present authors have previously derived criteria under which linear chains of
copies of one or more graphs have log-concave genus polynomials. Herein we
establish Ringel ladders as the first significant non-linear infinite family of
graphs known to have log-concave genus polynomials. We construct an algebraic
representation of self-bar-amalgamation as a matrix operation, to be applied to
a vector representation of the partitioned genus distribution of a symmetric
ladder. Analysis of the resulting genus polynomial involves the use of
Chebyshev polynomials. This paper continues our quest to affirm the
quarter-century-old conjecture that all graphs have log-concave genus
polynomials.Comment: 16 pages, 6 figure