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K-Independence Stable Graphs Upon Edge RemovalChellali, Mustapha, Haynes, Teresa W., Volkmann, Lutz 01 January 2010 (has links)
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 βk- -stable if βk(G - e) = βk(G) for every edge e of E(G). First we give a necessary and sufficient condition for βk--stable graphs. Then we establish four equivalent conditions for βk--stable trees.
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Ratios of Some Domination Parameters in TreesChellali, Mustapha, Favaron, Odile, Haynes, Teresa W., Raber, Dalila 06 September 2008 (has links)
We determine upper bounds on the ratios of several domination parameters in trees.
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