Domination with respect to nondegenerate and hereditary properties

Vladimir D. Samodivkin

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 $U \subseteq E (G)$ 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 $V (G) \cup E (G)$ 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. ...