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Generalized matrix graphs and completely independent critical cliques in any dimension

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Lattanzio J., Zheng Q.

Discussiones Mathematicae Graph Theory

2012

tom 32

nr 3

583-602

For natural numbers k and n, where 2 ≤ k ≤ n, the vertices of a graph are labeled using the elements of the k-fold Cartesian product Iₙ × Iₙ × ... × Iₙ. Two particular graph constructions will be given and the graphs so constructed are called generalized matrix graphs. Properties of generalized matrix graphs are determined and their application to completely independent critical cliques is investigated. It is shown that there exists a vertex critical graph which admits a family of k completely independent critical cliques for any k, where k ≥ 2. Some attention is given to this application and its relationship with the double-critical conjecture that the only vertex double-critical graph is the complete graph.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Lattanzio J.

1 Zheng Q.

1 2012

Wyniki wyszukiwania

Generalized matrix graphs and completely independent critical cliques in any dimension