Displaying similar documents to “Skein algebras of the solid torus and symmetric spatial graphs”

Symmetries of spatial graphs and Simon invariants

Ryo Nikkuni, Kouki Taniyama (2009)

Fundamenta Mathematicae

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An ordered and oriented 2-component link L in the 3-sphere is said to be achiral if it is ambient isotopic to its mirror image ignoring the orientation and ordering of the components. Kirk-Livingston showed that if L is achiral then the linking number of L is not congruent to 2 modulo 4. In this paper we study orientation-preserving or reversing symmetries of 2-component links, spatial complete graphs on 5 vertices and spatial complete bipartite graphs on 3 + 3 vertices in detail, and...

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.

The crossing numbers of join products of paths with graphs of order four

Marián Klešč, Stefan Schrötter (2011)

Discussiones Mathematicae Graph Theory

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Kulli and Muddebihal [V.R. Kulli, M.H. Muddebihal, Characterization of join graphs with crossing number zero, Far East J. Appl. Math. 5 (2001) 87-97] gave the characterization of all pairs of graphs which join product is planar graph. The crossing number cr(G) of a graph G is the minimal number of crossings over all drawings of G in the plane. There are only few results concerning crossing numbers of graphs obtained as join product of two graphs. In the paper, the exact values of crossing...

Isomorphic components of Kronecker product of bipartite graphs

Pranava K. Jha, Sandi Klavžar, Blaž Zmazek (1997)

Discussiones Mathematicae Graph Theory

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Weichsel (Proc. Amer. Math. Soc. 13 (1962) 47-52) proved that the Kronecker product of two connected bipartite graphs consists of two connected components. A condition on the factor graphs is presented which ensures that such components are isomorphic. It is demonstrated that several familiar and easily constructible graphs are amenable to that condition. A partial converse is proved for the above condition and it is conjectured that the converse is true in general.

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.

Some globally determined classes of graphs

Ivica Bošnjak, Rozália Madarász (2018)

Czechoslovak Mathematical Journal

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For a class of graphs we say that it is globally determined if any two nonisomorphic graphs from that class have nonisomorphic globals. We will prove that the class of so called CCB graphs and the class of finite forests are globally determined.

Supermagic Generalized Double Graphs 1

Jaroslav Ivančo (2016)

Discussiones Mathematicae Graph Theory

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A graph G is called supermagic if it admits a labelling of the edges by pairwise di erent consecutive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. In this paper we will introduce some constructions of supermagic labellings of some graphs generalizing double graphs. Inter alia we show that the double graphs of regular Hamiltonian graphs and some circulant graphs are supermagic.

Radio Graceful Hamming Graphs

Amanda Niedzialomski (2016)

Discussiones Mathematicae Graph Theory

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For k ∈ ℤ+ and G a simple, connected graph, a k-radio labeling f : V (G) → ℤ+ of G requires all pairs of distinct vertices u and v to satisfy |f(u) − f(v)| ≥ k + 1 − d(u, v). We consider k-radio labelings of G when k = diam(G). In this setting, f is injective; if f is also surjective onto {1, 2, . . . , |V (G)|}, then f is a consecutive radio labeling. Graphs that can be labeled with such a labeling are called radio graceful. In this paper, we give two results on the existence of radio...

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...

γ-labelings of complete bipartite graphs

Grady D. Bullington, Linda L. Eroh, Steven J. Winters (2010)

Discussiones Mathematicae Graph Theory

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Explicit formulae for the γ-min and γ-max labeling values of complete bipartite graphs are given, along with γ-labelings which achieve these extremes. A recursive formula for the γ-min labeling value of any complete multipartite is also presented.

Placing bipartite graphs of small size II

Beata Orchel (1996)

Discussiones Mathematicae Graph Theory

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In this paper we give all pairs of non mutually placeable (p,q)-bipartite graphs G and H such that 2 ≤ p ≤ q, e(H) ≤ p and e(G)+e(H) ≤ 2p+q-1.