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Double Roman domination subdivision number in graphs
Asian-European Journal of Mathematics, 2021For a graph [Formula: see text], a double Roman dominating function is a function [Formula: see text] having the property that if [Formula: see text], then vertex [Formula: see text] must have at least two neighbors assigned [Formula: see text] under [Formula: see text] or one neighbor with [Formula: see text], and if [Formula: see text], then vertex [
Amjadi, J., Sadeghi, H.
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Semitotal domination subdivision numbers of graphs
Journal of Discrete Mathematical Sciences and Cryptography, 2019A set D of vertices in an isolate-free graph G is a semitotal dominating set of G if D is a dominating set of G and every vertex in D is within distance 2 of another vertex of D.
Qin Chen, Yunfang Tang
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Roman domination subdivision number of graphs
Aequationes mathematicae, 2009A Roman dominating function on a graph G = (V, E) is a function $$f : V \rightarrow \{0, 1, 2\}$$ 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 weight of a Roman dominating function is
M. Atapour +2 more
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Some Graphs with Double Domination Subdivision Number Three
Graphs and Combinatorics, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Haoli +3 more
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TOTAL OUTER-CONNECTED DOMINATION SUBDIVISION NUMBERS IN GRAPHS
Discrete Mathematics, Algorithms and Applications, 2013A set S of vertices of a graph G is a total outer-connected dominating set if every vertex in V(G) is adjacent to some vertex in S and the subgraph G[V\S] induced by V\S is connected. The total outer-connected domination numberγ toc (G) is the minimum size of such a set.
Favaron, O. +2 more
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Game domination subdivision number of a graph
Journal of Combinatorial Optimization, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Favaron, O. +2 more
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Domination Uniform Subdivision Number of Graph
International Journal of Mathematics Trends and Technology, 2015Let G = (V, E) be a simple undirected graph. A subset D of V (G) is said to be dominating set if every vertex of V (G) − D is adjacent to at least one vertex in D. The minimum cardinality taken over all minimal dominating sets of G is the domination number of G and is denoted by γ(G). The domination uniform subdivision number of G is the least positive
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Secure domination subdivision number of a graph
Discrete Mathematics, Algorithms and Applications, 2019Let [Formula: see text] be a graph of order [Formula: see text] and size [Formula: see text] A dominating set [Formula: see text] of [Formula: see text] is called a secure dominating set if for each [Formula: see text] there exists [Formula: see text] such that [Formula: see text] is adjacent to [Formula: see text] and [Formula: see text] is a ...
Divya Rashmi, S. V. +2 more
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A New Bound on the Total Domination Subdivision Number
Graphs and Combinatorics, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Favaron, O. +3 more
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Domination subdivision numbers in graphs
2004A set \(S\) of vertices of a graph \(G\) is a dominating set if each vertex outside \(S\) has a neighbor in \(S\). The domination number \(\gamma(G)\) of \(G\) is the minimum cardinality of a dominating set of \(G\). An edge \(uv\) in \(G\) is subdivided if the edge \(uv\) is deleted, but a new vertex \(x\) is added, along with two new edges \(xu\) and
Favaron, Odile +2 more
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