Results 11 to 20 of about 612 (219)
DOMINATION NUMBER AND IDENTIFYING CODE NUMBER OF THE SUBDIVISION GRAPHS [PDF]
Journal of Algebraic SystemsLet $G=(V, E)$ be a simple graph. A set $C$ of vertices of $G$ is an identifying code of $G$ if for every two vertices $x$ and $y$ the sets $N_{G}[x] \cap C$ and $N_{G}[y] \cap C$ are non-empty and different.
Somaiya Ahmadi +2 more
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Total $k$-rainbow domination subdivision number in graphs [PDF]
Computer Science Journal of Moldova, 2020 A total $k$-rainbow dominating function (T$k$RDF) of $G$ is a function $f$ from the vertex set $V(G)$ to the set of all subsets of the set $\{1,\ldots,k\}$ such that (i) for any vertex $v\in V(G)$ with $f(v)=\emptyset$ the condition $\bigcup_{u \in N(v ...
Rana Khoeilar +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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Total Roman domination subdivision number in graphs [PDF]
Communications in Combinatorics and Optimization, 2020 A {\em Roman dominating function} on a graph $G$ is a function $f:V(G)\rightarrow \{0,1,2\}$ satisfying the condition that every vertex $u$ for which $f(u)=0$ is adjacent to at least one vertex $v$ for which $f(v)=2$.
Jafar Amjad
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Edge subdivision and edge multisubdivision versus some domination related parameters in generalized corona graphs [PDF]
Opuscula Mathematica, 2016 Given a graph \(G=(V,E)\), the subdivision of an edge \(e=uv\in E(G)\) means the substitution of the edge \(e\) by a vertex \(x\) and the new edges \(ux\) and \(xv\).
Magda Dettlaff +2 more
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On domination multisubdivision number of unicyclic graphs [PDF]
Opuscula Mathematica, 2018 The paper continues the interesting study of the domination subdivision number and the domination multisubdivision number. On the basis of the constructive characterization of the trees with the domination subdivision number equal to 3 given in [H. Aram,
Joanna Raczek
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Coronas and Domination Subdivision Number of a Graph [PDF]
Bulletin of the Malaysian Mathematical Sciences Society, 2016 In this paper, for a graph G and a family of partitions P of vertex neighborhoods of G, we define the general corona G \circ P of G. Among several properties of this new operation, we focus on application general coronas to a new kind of characterization of trees with the domination subdivision number equal to 3.
Dettlaff, M. +3 more
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Domination Subdivision Numbers
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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Block Graphs with Large Paired Domination Multisubdivision Number
Discussiones Mathematicae Graph Theory, 2021 The paired domination multisubdivision number of a nonempty graph G, denoted by msdpr(G), is the smallest positive integer k such that there exists an edge which must be subdivided k times to increase the paired domination number of G.
Mynhardt Christina M., 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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