Displaying similar documents to “A Characterization of Trees for a New Lower Bound on the K-Independence Number”

On Graphs with Disjoint Dominating and 2-Dominating Sets

Michael A. Henning, Douglas F. Rall (2013)

Discussiones Mathematicae Graph Theory

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A DD2-pair of a graph G is a pair (D,D2) of disjoint sets of vertices of G such that D is a dominating set and D2 is a 2-dominating set of G. Although there are infinitely many graphs that do not contain a DD2-pair, we show that every graph with minimum degree at least two has a DD2-pair. We provide a constructive characterization of trees that have a DD2-pair and show that K3,3 is the only connected graph with minimum degree at least three for which D ∪ D2 necessarily contains all vertices...

One-two descriptor of graphs

K. CH. Das, I. Gutman, D. Vukičević (2011)

Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques

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Strong Equality Between the Roman Domination and Independent Roman Domination Numbers in Trees

Mustapha Chellali, Nader Jafari Rad (2013)

Discussiones Mathematicae Graph Theory

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A Roman dominating function (RDF) on a graph G = (V,E) is a function f : V −→ {0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. The weight of an RDF is the value f(V (G)) = P u2V (G) f(u). An RDF f in a graph G is independent if no two vertices assigned positive values are adjacent. The Roman domination number R(G) (respectively, the independent Roman domination number iR(G)) is the minimum weight of an...

Saturation numbers for trees.

Faudree, Jill, Faudree, Ralph J., Gould, Ronald J., Jacobson, Michael S. (2009)

The Electronic Journal of Combinatorics [electronic only]

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