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On the doubly connected domination number of a graph
AbstractFor a given connected graph G = (V, E), a set $$D \subseteq V(G)$$ is a doubly connected dominating set if it is dominating and both 〈D〉 and 〈V (G)-D〉 are connected. The cardinality of theExpand
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Weakly convex and convex domination numbers
Two new domination parameters for a connected graph \(G\): the weakly convex domination number of \(G\) and the convex domination number of \(G\) are introduced. Relations between these parametersExpand
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Lower bound on the distance $k$-domination number of a tree
A subset D of vertices of a graph G = (V, E) is said to be a distance k -dominating set of G if every vertex of V — D is at distance at most k from some vertex of D. The minimum size of a distanceExpand
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Domination-Related Parameters in Rooted Product Graphs
A set S of vertices of a graph G is a dominating set in G if every vertex outside of S is adjacent to at least one vertex belonging to S. A domination parameter of G is related to those sets ofExpand
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Reconfiguring Minimum Dominating Sets in Trees
We provide tight bounds on the diameter of γ-graphs, which are reconfiguration graphs of the minimum dominating sets of a graph G. In particular, we prove that for any tree T of order n ≥ 3, theExpand
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On the partition dimension of trees
TLDR
The partition dimension of G is the minimum number of sets in any resolving partition of G . Expand
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Total Dominating Sets in Maximal Outerplanar Graphs
TLDR
We present an alternative proof of the result by Dorfling et al. establishing that any maximal outerplanar graph of order $$n \ge 5$$n≥5 has a total dominating set of size at most $$\lfloor \frac{2n}{5}\rfloor $$⌊2n5⌋, apart from two exceptions. Expand
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Bondage number of grid graphs
TLDR
The bondage number b(G) of a graph G is the cardinality of a smallest set of edges whose removal from G results in a graph with domination number greater than the domination number of G. Expand
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On the super domination number of lexicographic product graphs
TLDR
We obtain closed formulas and tight bounds for the super domination number of lexicographic product graphs in terms of invariants of the factor graphs involved in the product. Expand
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Nordhaus-Gaddum results for weakly convex domination number of a graph
TLDR
Nordhaus-Gaddum results for weakly convex domination number of a graph G are studied. Expand
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