Results 1 to 10 of about 612 (219)
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.
Shouliu Wei +2 more
exaly +4 more sources
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.
Guoliang Hao +2 more
exaly +4 more sources
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.
Saeed Kosari, R Khoeilar, H Karami
exaly +3 more sources
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),
Xiaoli Qiang +2 more
exaly +3 more sources
Domination Subdivision and Domination Multisubdivision Numbers of Graphs
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
doaj +4 more sources
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
doaj +4 more sources
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
doaj +2 more sources
Domination subdivision numbers of trees
Discrete Mathematics, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
S M Sheikholeslami, O Favaron
exaly +3 more sources
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
doaj +2 more sources
On the total domination subdivision numbers in graphs
Open Mathematics, 2010 Abstract A set S of vertices of a graph G = (V, E) without isolated vertex is a total dominating set if every vertex of V(G) is adjacent to some vertex in S. The total domination number γ t(G) is the minimum cardinality of a total dominating set of G. The total domination subdivision number sdγt
Sheikholeslami Seyed
doaj +3 more sources