A Characterization of Trees for a New Lower Bound on the K-Independence Number
Discussiones Mathematicae Graph Theory, Tome 33 (2013) no. 2, p. 395.

Voir la notice de l'article dans European Digital Mathematics Library

Let k be a positive integer and G = (V,E) a graph of order n. A subset S of V is a k-independent set of G if the maximum degree of the subgraph induced by the vertices of S is less or equal to k − 1. The maximum cardinality of a k-independent set of G is the k-independence number βk(G). In this paper, we show that for every graph [xxx], where χ(G), s(G) and Lv are the chromatic number, the number of supports vertices and the number of leaves neighbors of v, in the graph G, respectively. Moreover, we characterize extremal trees attaining these bounds.
Classification : 05C69
Mots-clés : domination, independence, k-independence, -independence 
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Nacéra Meddah; Mostafa Blidia. A Characterization of Trees for a New Lower Bound on the K-Independence Number. Discussiones Mathematicae Graph Theory, Tome 33 (2013) no. 2, p. 395. https://geodesic-test.mathdoc.fr/item/DMGT_2013__33_2_267566/