Displaying similar documents to “Domination with respect to nondegenerate and hereditary properties”

Domination with respect to nondegenerate properties: vertex and edge removal

Vladimir D. Samodivkin (2013)

Mathematica Bohemica

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In this paper we present results on changing and unchanging of the domination number with respect to the nondegenerate property 𝒫 , denoted by γ 𝒫 ( G ) , when a graph G is modified by deleting a vertex or deleting edges. A graph G is ( γ 𝒫 ( G ) , k ) 𝒫 -critical if γ 𝒫 ( G - S ) < γ 𝒫 ( G ) for any set S ⊊ V ( G ) with | S | = k . Properties of ( γ 𝒫 , k ) 𝒫 -critical graphs are studied. The plus bondage number with respect to the property 𝒫 , denoted b 𝒫 + ( G ) , is the cardinality of the smallest set of edges U ⊆ E ( G ) such that γ 𝒫 ( G - U ) > γ 𝒫 ( G ) . Some known results for ordinary domination and bondage...

The diameter of paired-domination vertex critical graphs

Michael A. Henning, Christina M. Mynhardt (2008)

Czechoslovak Mathematical Journal

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In this paper we continue the study of paired-domination in graphs introduced by Haynes and Slater (Networks (1998), 199–206). A paired-dominating set of a graph G with no isolated vertex is a dominating set of vertices whose induced subgraph has a perfect matching. The paired-domination number of G , denoted by γ pr ( G ) , is the minimum cardinality of a paired-dominating set of G . The graph G is paired-domination vertex critical if for every vertex v of G that is not adjacent to a vertex of...

Global domination and neighborhood numbers in Boolean function graph of a graph

T. N. Janakiraman, S. Muthammai, M. Bhanumathi (2005)

Mathematica Bohemica

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For any graph G , let V ( G ) and E ( G ) denote the vertex set and the edge set of G respectively. The Boolean function graph B ( G , L ( G ) , N I N C ) of G is a graph with vertex set V ( G ) ∪ E ( G ) and two vertices in B ( G , L ( G ) , N I N C ) are adjacent if and only if they correspond to two adjacent vertices of G , two adjacent edges of G or to a vertex and an edge not incident to it in G . In this paper, global domination number, total global domination number, global point-set domination number and neighborhood number for this graph are obtained. ...

Realizable triples for stratified domination in graphs

Ralucca Gera, Ping Zhang (2005)

Mathematica Bohemica

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A graph is 2 -stratified if its vertex set is partitioned into two classes, where the vertices in one class are colored red and those in the other class are colored blue. Let F be a 2 -stratified graph rooted at some blue vertex v . An F -coloring of a graph G is a red-blue coloring of the vertices of G in which every blue vertex v belongs to a copy of F rooted at v . The F -domination number γ F ( G ) is the minimum number of red vertices in an F -coloring of G . In this paper, we study F -domination...