Displaying similar documents to “Antidomatic number of a graph”

Induced-paired domatic numbers of graphs

Bohdan Zelinka (2002)

Mathematica Bohemica

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A subset D of the vertex set V ( G ) of a graph G is called dominating in G , if each vertex of G either is in D , or is adjacent to a vertex of D . If moreover the subgraph < D > of G induced by D is regular of degree 1, then D is called an induced-paired dominating set in G . A partition of V ( G ) , each of whose classes is an induced-paired dominating set in G , is called an induced-paired domatic partition of G . The maximum number of classes of an induced-paired domatic partition of G is the induced-paired...

A bound on the k -domination number of a graph

Lutz Volkmann (2010)

Czechoslovak Mathematical Journal

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Let G be a graph with vertex set V ( G ) , and let k ≥ 1 be an integer. A subset D ⊆ V ( G ) is called a if every vertex v ∈ V ( G ) - D has at least k neighbors in D . The k -domination number γ k ( G ) of G is the minimum cardinality of a k -dominating set in G . If G is a graph with minimum degree δ ( G ) ≥ k + 1 , then we prove that γ k + 1 ( G ) ≤ | V ( G ) | + γ k ( G ) 2 . In addition, we present a characterization of a special class of graphs attaining equality in this inequality.

The cobondage number of a graph

V.R. Kulli, B. Janakiram (1996)

Discussiones Mathematicae Graph Theory

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A set D of vertices in a graph G = (V,E) is a dominating set of G if every vertex in V-D is adjacent to some vertex in D. The domination number γ(G) of G is the minimum cardinality of a dominating set. We define the cobondage number b c ( G ) of G to be the minimum cardinality among the sets of edges X ⊆ P₂(V) - E, where P₂(V) = X ⊆ V:|X| = 2 such that γ(G+X) < γ(G). In this paper, the exact values of bc(G) for some standard graphs are found and some bounds are obtained. Also, a Nordhaus-Gaddum...

Homogeneously embedding stratified graphs in stratified graphs

Gary Chartrand, Donald W. Vanderjagt, Ping Zhang (2005)

Mathematica Bohemica

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A 2-stratified graph G is a graph whose vertex set has been partitioned into two subsets, called the strata or color classes of G . Two 2 -stratified graphs G and H are isomorphic if there exists a color-preserving isomorphism φ from G to H . A 2 -stratified graph G is said to be homogeneously embedded in a 2 -stratified graph H if for every vertex x of G and every vertex y of H , where x and y are colored the same, there exists an induced 2 -stratified subgraph H ' of H containing y and a color-preserving...