Displaying similar documents to “On Graphs with Disjoint Dominating and 2-Dominating Sets”

Steiner distance in graphs

Gary Chartrand, Ortrud R. Oellermann, Song Lin Tian, Hung Bin Zou (1989)

Časopis pro pěstování matematiky

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On Unique Minimum Dominating Sets in Some Cartesian Product Graphs

Jason T. Hedetniemi (2015)

Discussiones Mathematicae Graph Theory

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Unique minimum vertex dominating sets in the Cartesian product of a graph with a complete graph are considered. We first give properties of such sets when they exist. We then show that when the first factor of the product is a tree, consideration of the tree alone is sufficient to determine if the product has a unique minimum dominating set.

Extended trees of graphs

Bohdan Zelinka (1994)

Mathematica Bohemica

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An extended tree of a graph is a certain analogue of spanning tree. It is defined by means of vertex splitting. The properties of these trees are studied, mainly for complete graphs.

Two Short Proofs on Total Domination

Allan Bickle (2013)

Discussiones Mathematicae Graph Theory

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A set of vertices of a graph G is a total dominating set if each vertex of G is adjacent to a vertex in the set. The total domination number of a graph Υt (G) is the minimum size of a total dominating set. We provide a short proof of the result that Υt (G) ≤ 2/3n for connected graphs with n ≥ 3 and a short characterization of the extremal graphs.