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

Discussiones Mathematicae Graph Theory (2013)

- Volume: 33, Issue: 2, page 395-410
- ISSN: 2083-5892

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topNacéra Meddah, and Mostafa Blidia. "A Characterization of Trees for a New Lower Bound on the K-Independence Number." Discussiones Mathematicae Graph Theory 33.2 (2013): 395-410. <http://eudml.org/doc/267566>.

@article{NacéraMeddah2013,

abstract = {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.},

author = {Nacéra Meddah, Mostafa Blidia},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {domination; independence; k-independence; -independence},

language = {eng},

number = {2},

pages = {395-410},

title = {A Characterization of Trees for a New Lower Bound on the K-Independence Number},

url = {http://eudml.org/doc/267566},

volume = {33},

year = {2013},

}

TY - JOUR

AU - Nacéra Meddah

AU - Mostafa Blidia

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

JO - Discussiones Mathematicae Graph Theory

PY - 2013

VL - 33

IS - 2

SP - 395

EP - 410

AB - 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.

LA - eng

KW - domination; independence; k-independence; -independence

UR - http://eudml.org/doc/267566

ER -

## References

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