Results 11 to 20 of about 9,132,004 (247)
Domination Subdivision and Domination Multisubdivision Numbers of Graphs [PDF]
Discussiones Mathematicae Graph Theory, 2019 The domination subdivision number sd(G) of a graph G is the minimum number of edges that must be subdivided (where an edge can be subdivided at most once) in order to increase the domination number of G. It has been shown [10] that sd(T) ≤ 3 for any tree
Dettlaff Magda +2 more
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The convex domination subdivision number of a graph
Communications in Combinatorics and Optimization, 2016 Let $G=(V,E)$ be a simple graph. A set $D\subseteq V$ is a dominating set of $G$ if every vertex in $V\setminus D$ has at least one neighbor in $D$. The distance $d_G(u,v)$ between two vertices $u$ and $v$ is the length of a shortest $(u,v)$-
M. Dettlaff +3 more
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Roman game domination subdivision number of a graph [PDF]
Transactions on Combinatorics, 2013 A {em Roman dominating function} on a graph $G = (V ,E)$ is a function $f : Vlongrightarrow {0, 1, 2}$ satisfying the condition that every vertex $v$ for which $f (v) = 0$ is adjacent to at least one vertex $u$ for which $f (u) = 2$. The {em weight} of a
Jafar Amjadi +3 more
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Domination Subdivision Numbers [PDF]
Discussiones Mathematicae Graph Theory, 2001 A set \(S\) of vertices of a graph \(G\) is a dominating set if every vertex of \(V(G)-S\) is adjacent to some vertex in \(S\). The domination number \(\gamma(G)\) is the minimum cardinality of a dominating set of \(G\), and the domination subdivision number \(\text{sd}_{\gamma}(G)\) is the minimum number of edges that must be subdivided (each edge in \
Teresa W. Haynes +5 more
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Weakly connected domination subdivision numbers [PDF]
Discussiones Mathematicae Graph Theory, 2008 A set D of vertices in a graph G = (V, E) is a weakly connected dominating set of G if D is dominating in G and the subgraph weakly induced by D is connected. The weakly connected domination number of G is the minimum cardinality of a weakly connected dominating set of G.
Raczek, Joanna
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Trees whose 2-domination subdivision number is 2 [PDF]
Opuscula Mathematica, 2012 A set \(S\) of vertices in a graph \(G = (V,E)\) is a \(2\)-dominating set if every vertex of \(V\setminus S\) is adjacent to at least two vertices of \(S\). The \(2\)-domination number of a graph \(G\), denoted by \(\gamma_2(G)\), is the minimum size of
M. Atapour +2 more
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Total domination subdivision numbers of graphs [PDF]
Discussiones Mathematicae Graph Theory, 2004 Summary: A set \(S\) of vertices in a graph \(G=(V,E)\) is a total dominating set of \(G\) if every vertex of \(V\) is adjacent to a vertex in \(S\). The total domination number of \(G\) is the minimum cardinality of a total dominating set of \(G\). The total domination subdivision number of \(G\) is the minimum number of edges that must be subdivided (
Teresa W. Haynes +2 more
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Disjunctive Total Domination Subdivision Number of Graphs
Fundamenta Informaticae, 2020 A set S ⊆ V (G) is a disjunctive total dominating set of G if every vertex has a neighbor in S or has at least two vertices in S at distance 2 from it. The disjunctive total domination number is the minimum cardinality of a disjunctive total dominating set in G. We define the disjunctive total domination subdivision number of G as the minimum number of
Ciftci, Canan, Aytac, Vecdi
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Total Domination Multisubdivision Number of a Graph [PDF]
Discussiones Mathematicae Graph Theory, 2015 The domination multisubdivision number of a nonempty graph G was defined in [3] as the minimum positive integer k such that there exists an edge which must be subdivided k times to increase the domination number of G.
Avella-Alaminos Diana +3 more
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Domination and independence subdivision numbers of graphs [PDF]
Discussiones Mathematicae Graph Theory, 2000 A subset \(S\) of the vertex set \(V(G)\) of a graph \(G\) is called dominating in \(G\), if each vertex of \(G\) either is in \(S\), or is adjacent to a vertex of \(S\). A set \(S\subseteq V(G)\) is independent in \(G\), if no two vertices of \(S\) are adjacent in \(G\).
Teresa W. Haynes +2 more
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