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k-independence stable graphs upon edge removal

100%

Chellali M., Haynes T., Volkmann L.

Discussiones Mathematicae Graph Theory

2010

tom 30

nr 2

265-274

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.

A Characterization of Trees for a New Lower Bound on the K-Independence Number

80%

Meddah N., Blidia M.

Discussiones Mathematicae Graph Theory

2013

tom 33

nr 2

395-410

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.

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2 Discussiones Mathematicae Graph Theory

1 Blidia M.

1 Chellali M.

1 Haynes T.

1 Meddah N.

1 Volkmann L.

1 2013

1 2010

Wyniki wyszukiwania

k-independence stable graphs upon edge removal

A Characterization of Trees for a New Lower Bound on the K-Independence Number