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Fundamentals of domination in graphs
TLDR
Bounds on the domination number domination, independence and irredundance efficiency, redundancy and the duals changing and unchanging domination conditions on the dominating set varieties of domination multiproperty and multiset parameters sums and products of parameters dominating functions frameworks for domination domination complexity and algorithms. Expand
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Domination in Graphs Applied to Electric Power Networks
TLDR
The problem of monitoring an electric power system by placing as few measurement devices in the system as possible is closely related to vertex covering and dominating set problems in graphs. Expand
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Domination in graphs : advanced topics
LP-duality, complementarity and generality of graphical subset parameters dominating functions in graphs fractional domination and related parameters majority domination and its generalizationsExpand
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Paired‐domination in graphs
In a graph G = (V, E) if we think of each vertex s as the possible location for a guard capable of protecting each vertex in its closed neighborhood N[s], then “domination” requires every vertex toExpand
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Double Domination in Graphs
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Global Defensive Alliances in Graphs
TLDR
A defensive alliance in a graph G =( V,E) is a set of vertices S V satisfying the condition that for every vertex v 2 S, the number of neighbors v has in S plus one (counting v) is at least as large as the number the neighbors it has in V S. Expand
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Broadcasts in graphs
TLDR
We say that a function f : V → {0, 1, ..., diam(G)} is a broadcast if for every vertex v ∈ V, f(v) ≤ e(v). Expand
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Double Roman domination
TLDR
A double Roman dominating function is a function f with the property that if f ( v ) = 0 , then vertex v must have at least two neighbors assigned 2 under f or one neighbor with f ( w ) = 3 under f . Expand
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Roman {2}-domination
TLDR
In this paper, we initiate the study of a variant of Roman dominating functions. Expand
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The diameter of total domination vertex critical graphs
TLDR
We characterize the connected graphs with minimum degree one that are γ t -critical and we obtain sharp bounds on their maximum diameter. Expand
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