Displaying similar documents to “Homogeneously embedding stratified graphs in stratified graphs”

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...

Distance in stratified graphs

Gary Chartrand, Lisa Hansen, Reza Rashidi, Naveed Sherwani (2000)

Czechoslovak Mathematical Journal

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A graph G is stratified if its vertex set is partitioned into classes, called strata. If there are k strata, then G is k -stratified. These graphs were introduced to study problems in VLSI design. The strata in a stratified graph are also referred to as color classes. For a color X in a stratified graph G , the X -eccentricity e X ( v ) of a vertex v of G is the distance between v and an X -colored vertex furthest from v . The minimum X -eccentricity among the vertices of G is the X -radius r a d X G of G ...

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.