منابع مشابه
Genus distributions of star-ladders
Star-ladder graphs were introduced by Gross in his development of a quadratic-time algorithm for the genus distribution of a cubic outerplanar graph. This paper derives a formula for the genus distribution of star-ladder graphs, using Mohar’s overlap matrix and Chebyshev polynomials. Newly developed methods have led to a number of recent papers that derive genus distributions and total embeddin...
متن کاملTotal Embedding Distributions of Circular Ladders
where ai is the number of embeddings, for i = 0, 1, . . ., into the orientable surface Si, and bj is the number of embeddings, for j = 1, 2, . . ., into the non-orientable surface Nj . The sequence {ai(G)|i ≥ 0} ⋃ {bj(G)|j ≥ 1} is called the total embedding distribution of the graph G; it is known for relatively few classes of graphs, compared to the genus distribution {ai(G)|i ≥ 0}. The circul...
متن کاملTotal embedding distributions of Ringel ladders
The total embedding distributions of a graph is consisted of the orientable embeddings and nonorientable embeddings and have been know for few classes of graphs. The genus distribution of Ringel ladders is determined in [Discrete Mathematics 216 (2000) 235-252] by E.H. Tesar. In this paper, the explicit formula for non-orientable embeddings of Ringel ladders is obtained.
متن کاملLog-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 t...
متن کاملExplicit geodesic flow-invariant distributions using SL2(ℝ)-representation ladders
An explicit construction of a geodesic flow-invariant distribution lying in the discrete series of weight 2k isotopic component is found, using techniques from representation theory of SL2(R). It is found that the distribution represents an AC measure on the unit tangent bundle of the hyperbolic plane minus an explicit singular set. Finally, via an averaging argument, a geodesic flow-invariant ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2012
ISSN: 0012-365X
DOI: 10.1016/j.disc.2012.07.004