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

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 pape...

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Main Authors:	Meddah Nacéra, Blidia Mostafa
Format:	Article
Language:	English
Published:	Sciendo 2013-05-01
Series:	Discussiones Mathematicae Graph Theory
Subjects:	domination independence k-independence
Online Access:	https://doi.org/10.7151/dmgt.1677

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spelling	doaj-125d7b7833794fd3bc10bd0573f767242021-09-05T17:20:20ZengSciendoDiscussiones Mathematicae Graph Theory2083-58922013-05-0133239541010.7151/dmgt.1677A Characterization of Trees for a New Lower Bound on the K-Independence NumberMeddah Nacéra0Blidia Mostafa1LAMDA-RO, Department of Mathematics University of Blida B.P. 270, Blida, AlgeriaLAMDA-RO, Department of Mathematics University of Blida B.P. 270, Blida, AlgeriaLet 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.https://doi.org/10.7151/dmgt.1677dominationindependencek-independence
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Meddah Nacéra Blidia Mostafa
spellingShingle	Meddah Nacéra Blidia Mostafa A Characterization of Trees for a New Lower Bound on the K-Independence Number Discussiones Mathematicae Graph Theory domination independence k-independence
author_facet	Meddah Nacéra Blidia Mostafa
author_sort	Meddah Nacéra
title	A Characterization of Trees for a New Lower Bound on the K-Independence Number
title_short	A Characterization of Trees for a New Lower Bound on the K-Independence Number
title_full	A Characterization of Trees for a New Lower Bound on the K-Independence Number
title_fullStr	A Characterization of Trees for a New Lower Bound on the K-Independence Number
title_full_unstemmed	A Characterization of Trees for a New Lower Bound on the K-Independence Number
title_sort	characterization of trees for a new lower bound on the k-independence number
publisher	Sciendo
series	Discussiones Mathematicae Graph Theory
issn	2083-5892
publishDate	2013-05-01
description	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.
topic	domination independence k-independence
url	https://doi.org/10.7151/dmgt.1677
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A Characterization of Trees for a New Lower Bound on the K-Independence Number

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