Validity up to complementation in graph theory
T. McKee (1983)
Fundamenta Mathematicae
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T. McKee (1983)
Fundamenta Mathematicae
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Proskurowski, Andrzej, Telle, Jan Arne (1999)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
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Vladimír Puš (1988)
Commentationes Mathematicae Universitatis Carolinae
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Jan Kratochvíl (1995)
Commentationes Mathematicae Universitatis Carolinae
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In this note, we introduce the notion of -Ramsey classes of graphs and we reveal connections to intersection dimensions of 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.
Alain Bretto, Alain Faisant (2005)
Mathematica Slovaca
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S. Shalchi, A. Erfanian, M. Farrokhi DG (2017)
Open Mathematics
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The θ-commutators of elements of a group with respect to an automorphism are introduced and their properties are investigated. Also, corresponding to θ-commutators, we define the θ-non-commuting graphs of groups and study their correlations with other notions. Furthermore, we study independent sets in θ-non-commuting graphs, which enable us to evaluate the chromatic number of such graphs.
Sandi Klavžar, Matjaz Kovse (2007)
Discussiones Mathematicae Graph Theory
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The Θ-graph Θ(G) of a partial cube G is the intersection graph of the equivalence classes of the Djoković-Winkler relation. Θ-graphs that are 2-connected, trees, or complete graphs are characterized. In particular, Θ(G) is complete if and only if G can be obtained from K₁ by a sequence of (newly introduced) dense expansions. Θ-graphs are also compared with familiar concepts of crossing graphs and τ-graphs.