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Displaying similar documents to “A study about the Tutte polynomials of benzenoid chains”

On chromaticity of graphs

Ewa Łazuka (1995)

Discussiones Mathematicae Graph Theory

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In this paper we obtain the explicit formulas for chromatic polynomials of cacti. From the results relating to cacti we deduce the analogous formulas for the chromatic polynomials of n-gon-trees. Besides, we characterize unicyclic graphs by their chromatic polynomials. We also show that the so-called clique-forest-like graphs are chromatically equivalent.

On sectional Newtonian graphs

Zening Fan, Suo Zhao (2020)

Czechoslovak Mathematical Journal

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In this paper, we introduce the so-called sectional Newtonian graphs for univariate complex polynomials, and study some properties of those graphs. In particular, we list all possible sectional Newtonian graphs when the degrees of the polynomials are less than five, and also show that every stable gradient graph can be realized as a polynomial sectional Newtonian graph.

An attractive class of bipartite graphs

Rodica Boliac, Vadim Lozin (2001)

Discussiones Mathematicae Graph Theory

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In this paper we propose a structural characterization for a class of bipartite graphs defined by two forbidden induced subgraphs. We show that the obtained characterization leads to polynomial-time algorithms for several problems that are NP-hard in general bipartite graphs.

Chromatic polynomials of hypergraphs

Mieczysław Borowiecki, Ewa Łazuka (2000)

Discussiones Mathematicae Graph Theory

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In this paper we present some hypergraphs which are chromatically characterized by their chromatic polynomials. It occurs that these hypergraphs are chromatically unique. Moreover we give some equalities for the chromatic polynomials of hypergraphs generalizing known results for graphs and hypergraphs of Read and Dohmen.

Jones polynomials, volume and essential knot surfaces: a survey

David Futer, Efstratia Kalfagianni, Jessica S. Purcell (2014)

Banach Center Publications

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This paper is a brief overview of recent results by the authors relating colored Jones polynomials to geometric topology. The proofs of these results appear in the papers [18, 19], while this survey focuses on the main ideas and examples.

Dominant-matching graphs

Igor' E. Zverovich, Olga I. Zverovich (2004)

Discussiones Mathematicae Graph Theory

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We introduce a new hereditary class of graphs, the dominant-matching graphs, and we characterize it in terms of forbidden induced subgraphs.

Factoring directed graphs with respect to the cardinal product in polynomial time II

Wilfried Imrich, Werner Klöckl (2010)

Discussiones Mathematicae Graph Theory

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By a result of McKenzie [7] all finite directed graphs that satisfy certain connectivity conditions have unique prime factorizations with respect to the cardinal product. McKenzie does not provide an algorithm, and even up to now no polynomial algorithm that factors all graphs satisfying McKenzie's conditions is known. Only partial results [1,3,5] have been published, all of which depend on certain thinness conditions of the graphs to be factored. In this paper we...