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On the Paired-Domination Subdivision Number of Trees [PDF]
Mathematics, 2021 A paired-dominating set of a graph G without isolated vertices is a dominating set of vertices whose induced subgraph has perfect matching. The minimum cardinality of a paired-dominating set of G is called the paired-domination number γpr(G) of G.
Guoliang Hao +2 more
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On the Paired-Domination Subdivision Number of a Graph [PDF]
Mathematics, 2021 In order to increase the paired-domination number of a graph G, the minimum number of edges that must be subdivided (where each edge in G can be subdivided no more than once) is called the paired-domination subdivision number sdγpr(G) of G.
Mustapha Chellali +2 more
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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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Domination subdivision numbers of trees [PDF]
Discrete Mathematics, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
S M Sheikholeslami, O Favaron
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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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On a conjecture concerning total domination subdivision number in graphs
AKCE International Journal of Graphs and Combinatorics, 2021 Let be the total domination number and let be the total domination subdivision number of a graph G with no isolated vertex. In this paper, we show that for some classes of graphs G, which partially solve the conjecture presented by Favaron et al.
Rana Khoeilar +2 more
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A Note on the Paired-Domination Subdivision Number of Trees
Mathematics, 2021 For a graph G with no isolated vertex, let γpr(G) and sdγpr(G) denote the paired-domination and paired-domination subdivision numbers, respectively. In this note, we show that if T is a tree of order n≥4 different from a healthy spider (subdivided star),
Mustapha Chellali +2 more
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Triple Roman domination subdivision number in graphs [PDF]
Computer Science Journal of Moldova, 2022 For a graph $G=(V, E)$, a triple Roman domination function is a function $f: V(G)\longrightarrow\{0, 1, 2, 3, 4\}$ having the property that for any vertex $v\in V(G)$, if $f(v)
Jafar Amjadi, Hakimeh Sadeghi
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On [k]-Roman domination subdivision number of graphs
AKCE International Journal of Graphs and Combinatorics, 2022 Let [Formula: see text] be an integer and G a simple graph with vertex set V(G). Let f be a function that assigns labels from the set [Formula: see text] to the vertices of G.
K. Haghparast +3 more
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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.
Paweł Zylinski +2 more
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