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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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Total dominator chromatic number of k-subdivision of graphs
The Art of Discrete and Applied Mathematics, 2022 Let $G$ be a simple graph. A total dominator coloring of $G$, is a proper coloring of the vertices of $G$ in which each vertex of the graph is adjacent to every vertex of some color class. The total dominator chromatic (TDC) number $ _d^t(G)$ of $G$, is the minimum number of colors among all total dominator coloring of $G$. For any $k \in \mathbb{N}$,
Alikhani, Saeid +2 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 \
Haynes, Teresa W. +5 more
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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.
Shouliu Wei +4 more
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Domination subdivision and domination multisubdivision numbers of graph
Discussiones Mathematicae Graph Theory, 2019 12 pages, 2 ...
Dettlaff Magda +2 more
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Domination subdivision numbers of trees
Discrete Mathematics, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Aram, H. +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 $(u,v)$-path in $G$. An $(u,v)$-path of length $d_G(u,v)$ is called an $(u,v)$-geodesic.
Dettlaff, M. +3 more
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Total domination subdivision numbers of trees
Discrete Mathematics, 2004 The total domination subdivision number \(\text{ sd}_{\gamma_t}(G)\) of a graph \(G\) is the minimum number of edges whose subdivision increases the total domination number \({\gamma_t}(G)\) of \(G\). \textit{T. W. Haynes} et al. [J. Comb. Math. Comb. Comput.
Haynes, Teresa W. +2 more
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Triple Roman domination subdivision number in graphs
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 $f(v)<3$, then $f(\mbox{AN}[v])\geq|\mbox{AN}(v)|+3$, where $\mbox{AN}(v)=\{w\in N(v)\mid f(w)\geq1\}$ and $\mbox{AN}[v]=\mbox{AN}(v)\cup\{v\}$.
Amjadi, J., Sadeghi, H.
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Total domination subdivision numbers of graphs
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 (
Haynes, Teresa W. +2 more
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