Necessity of the condition is clear, since an edgeless graph has a unique dominat- ing set. Sufficiency follows from the fact that each maximal stable set ...
We define the P-stability number of a graph G, αP(G), as the maximum cardinality of a P-set in G. A P-dominating set in a graph is a dominating P-set.
Let P be a class of graphs. A P-set in a graph G is a vertex subset X such that. G(X) ∈ P. We define the P-stability number of a graph G, αP(G), ...
Apr 28, 2009 · In this paper we establish best possible bounds on the ratios of the packing numbers of any (connected) graph to its six domination-related ...
These parameters return the maximum/minimum cardinality of a set satisfying some property. However, they can be generalized for graphs with weighted vertices ...
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M.A. Henning and H.C. Swart, Bounds on a generalized total domination parameter, J. Combin. Math. Combin. Comput., to appear. Google Scholar.
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Nov 3, 2023 · Sós [6], states that graphs with the property that every two vertices have exactly one neighbour in common are exactly the friendship graphs.
A dominating set D is said to be a total dominating set if every vertex in V is adjacent to some vertex in D. The total domination number of G denoted by γt. (G) ...
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In this paper we establish best possible bounds on the ratios of the packing numbers of any (connected) graph to its six domination-related parameters (the ...
In this framework, we study trade-offs between the stability parameter k and the approximation ratio that can be achieved. Ideally, we would like to have a so- ...