Spanning trees with many leaves and average distance.

DeLaViña, Ermelinda; Waller, Bill

Displaying similar documents to “Spanning trees with many leaves and average distance.”

The Distance Roman Domination Numbers of Graphs

Hamideh Aram, Sepideh Norouzian, Seyed Mahmoud Sheikholeslami (2013)

Discussiones Mathematicae Graph Theory

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Let k be a positive integer, and let G be a simple graph with vertex set V (G). A k-distance Roman dominating function on G is a labeling f : V (G) → {0, 1, 2} such that for every vertex with label 0, there is a vertex with label 2 at distance at most k from each other. The weight of a k-distance Roman dominating function f is the value w(f) =∑v∈V f(v). The k-distance Roman domination number of a graph G, denoted by γkR (D), equals the minimum weight of a k-distance Roman dominating...

A note on $K_{Δ + 1}^{-}$ -free precolouring with $Δ$ colours.

Rackham, Tom (2009)

The Electronic Journal of Combinatorics [electronic only]

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Embedding a forest in a graph.

Goldberg, Mark K., Magdon-Ismail, Malik (2011)

The Electronic Journal of Combinatorics [electronic only]

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A new upper bound on the total domination number of a graph.

Henning, Michael A., Yeo, Anders (2007)

The Electronic Journal of Combinatorics [electronic only]

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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...