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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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 |
work_keys_str_mv |
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