Displaying similar documents to “On the p-domination number of cactus graphs”

γ-graphs of graphs

Gerd H. Fricke, Sandra M. Hedetniemi, Stephen T. Hedetniemi, Kevin R. Hutson (2011)

Discussiones Mathematicae Graph Theory

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A set S ⊆ V is a dominating set of a graph G = (V,E) if every vertex in V -S is adjacent to at least one vertex in S. The domination number γ(G) of G equals the minimum cardinality of a dominating set S in G; we say that such a set S is a γ-set. In this paper we consider the family of all γ-sets in a graph G and we define the γ-graph G(γ) = (V(γ), E(γ)) of G to be the graph whose vertices V(γ) correspond 1-to-1 with the γ-sets of G, and two γ-sets, say D₁ and D₂, are adjacent in E(γ)...

Paired-domination

S. Fitzpatrick, B. Hartnell (1998)

Discussiones Mathematicae Graph Theory

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We are interested in dominating sets (of vertices) with the additional property that the vertices in the dominating set can be paired or matched via existing edges in the graph. This could model the situation of guards or police where each has a partner or backup. This paper will focus on those graphs in which the number of matched pairs of a minimum dominating set of this type equals the size of some maximal matching in the graph. In particular, we characterize the leafless graphs of...

Graphs with disjoint dominating and paired-dominating sets

Justin Southey, Michael Henning (2010)

Open Mathematics

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A dominating set of a graph is a set of vertices such that every vertex not in the set is adjacent to a vertex in the set, while a paired-dominating set of a graph is a dominating set such that the subgraph induced by the dominating set contains a perfect matching. In this paper, we show that no minimum degree is sufficient to guarantee the existence of a disjoint dominating set and a paired-dominating set. However, we prove that the vertex set of every cubic graph can be partitioned...

Supermagic Graphs Having a Saturated Vertex

Jaroslav Ivančo, Tatiana Polláková (2014)

Discussiones Mathematicae Graph Theory

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A graph is called supermagic if it admits a labeling of the edges by pairwise different consecutive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. In this paper we establish some conditions for graphs with a saturated vertex to be supermagic. Inter alia we show that complete multipartite graphs K1,n,n and K1,2,...,2 are supermagic.

On the Totalk-Domination in Graphs

Sergio Bermudo, Juan C. Hernández-Gómez, José M. Sigarreta (2018)

Discussiones Mathematicae Graph Theory

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Let G = (V, E) be a graph; a set S ⊆ V is a total k-dominating set if every vertex v ∈ V has at least k neighbors in S. The total k-domination number γkt(G) is the minimum cardinality among all total k-dominating sets. In this paper we obtain several tight bounds for the total k-domination number of a graph. In particular, we investigate the relationship between the total k-domination number of a graph and the order, the size, the girth, the minimum and maximum degree, the diameter,...

Nullity of Graphs

Bijana Borovićanin, Ivan Gutman (2009)

Zbornik Radova

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