Geodesic
k-independence stable graphs upon edge removal
Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 2, pp. 265-274 Cet article a éte moissonné depuis la source Library of Science

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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 condition for β¯ₖ-stable graphs. Then we establish four equivalent conditions for β¯ₖ-stable trees.
Keywords: k-independence stable graphs, k-independence 
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Chellali, Mustapha; Haynes, Teresa; Volkmann, Lutz. k-independence stable graphs upon edge removal. Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 2, pp. 265-274. http://geodesic.mathdoc.fr/item/DMGT_2010_30_2_a7/

[1] M. Blidia, M. Chellali and L. Volkmann, Some bounds on the p-domination number in trees, Discrete Math. 306 (2006) 2031-2037, doi: 10.1016/j.disc.2006.04.010.

[2] J.F. Fink and M.S. Jacobson, n-domination in graphs, in: Graph Theory with Applications to Algorithms and Computer (John Wiley and sons, New York, 1985) 283-300.

[3] G. Gunther, B. Hartnell and D.F. Rall, Graphs whose vertex independence number is unaffected by single edge addition or deletion, Discrete Appl. Math. 46 (1993) 167-172, doi: 10.1016/0166-218X(93)90026-K.