Total domination critical and stable graphs upon edge removal
نویسندگان
چکیده
منابع مشابه
Double domination stable graphs upon edge removal
In a graph G = (V (G), E(G)), a vertex dominates itself and its neighbors. A subset S of V (G) is a double dominating set if every vertex of V (G) is dominated at least twice by the vertices of S. The double domination number of G is the minimum cardinality among all double dominating sets of G. We consider the effects of edge removal on the double domination number of a graph. We give a necess...
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In a graph a vertex is said to dominate itself and all its neighbors. A double dominating set of a graph G is a subset of vertices that dominates every vertex of G at least twice. The double domination number of G, denoted γ×2(G), is the minimum cardinality among all double dominating sets ofG. We consider the effects of vertex removal on the double domination number of a graph. A graph G is γ×...
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For any of the basic domination parameters ir, , i, , or IR, we study graphs for which increases whenever an edge is removed ( -ER-critical graphs) and graphs for which decreases whenever an edge is removed ( −-ER-critical graphs). The latter case is only possible if = i or (perhaps) = ir. We give examples of classes of -ER-critical graphs for an upper domination parameter and characterize thes...
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In a graph, a vertex is said to dominate itself and all its neighbors. A double dominating set of a graph G is a subset of vertices that dominates every vertex of G at least twice. The double domination number γ×2(G) is the minimum cardinality of a double dominating set of G. A graph G without isolated vertices is called edge removal critical with respect to double domination, or just γ×2-criti...
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Let k be a positive integer and G = (V (G), E(G)) a graph. A subset S of V (G) is a k-independent set of G if the subgraph induced by the vertices of S has maximum degree at most k−1. The maximum cardinality of a k-independent set of G is the k-independence number βk(G). A graph G is called β − k -stable if βk(G − e) = βk(G) for every edge e of E(G). First we give a necessary and sufficient con...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2010
ISSN: 0166-218X
DOI: 10.1016/j.dam.2010.06.003