On strongly connected orientations of graphs
Matúš Harminc (1999)
Discussiones Mathematicae Graph Theory
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Matúš Harminc (1999)
Discussiones Mathematicae Graph Theory
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Frank, András (1998)
Documenta Mathematica
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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.
Gary Chartrand, Hudson V. Kronk, Seymour Schuster (1973)
Colloquium Mathematicae
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Liskovets, Valery A. (2000)
Journal of Integer Sequences [electronic only]
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Mirko Lepović (1991)
Publications de l'Institut Mathématique
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Benjamin Espinoza, Paul Gartside, Ana Mamatelashvili (2013)
Colloquium Mathematicae
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A space is n-arc connected (n-ac) if any family of no more than n-points are contained in an arc. For graphs the following are equivalent: (i) 7-ac, (ii) n-ac for all n, (iii) continuous injective image of a closed subinterval of the real line, and (iv) one of a finite family of graphs. General continua that are ℵ₀-ac are characterized. The complexity of characterizing n-ac graphs for n = 2,3,4,5 is determined to be strictly higher than that of the stated characterization of 7-ac graphs. ...
Bretto, A. (1999)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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Zdzisław Skupień (2007)
Discussiones Mathematicae Graph Theory
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W. Wessel (1987)
Applicationes Mathematicae
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Risto Šokarovski (1977)
Publications de l'Institut Mathématique
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Li, Xueliang, Liu, Yan (2008)
The Electronic Journal of Combinatorics [electronic only]
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S. F. Kapoor, Linda M. Lesniak (1976)
Colloquium Mathematicae
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José D. Alvarado, Simone Dantas, Dieter Rautenbach (2017)
Discussiones Mathematicae Graph Theory
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For a graph G, let R(G) and yr2(G) denote the Roman domination number of G and the 2-rainbow domination number of G, respectively. It is known that yr2(G) ≤ R(G) ≤ 3/2yr2(G). Fujita and Furuya [Difference between 2-rainbow domination and Roman domination in graphs, Discrete Appl. Math. 161 (2013) 806-812] present some kind of characterization of the graphs G for which R(G) − yr2(G) = k for some integer k. Unfortunately, their result does not lead to an algorithm that allows to recognize...