The k-distance chromatic number of trees and cycles

For any positive integer k, a k-distance coloring of a graph G is a vertex coloring of G in which no two vertices at distance less than or equal to k receive the same color. The k-distance chromatic number of G, denoted by χkGis the smallest integer α for which G has a k-distance α-coloring. In this...

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Main Authors:	Niranjan P.K., Srinivasa Rao Kola
Format:	Article
Language:	English
Published:	Taylor & Francis Group 2019-08-01
Series:	AKCE International Journal of Graphs and Combinatorics
Online Access:	http://www.sciencedirect.com/science/article/pii/S0972860017301056

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spelling	doaj-795822f944d94777bb11c37d7bbbfaf32020-11-25T02:56:49ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002019-08-01162230235The k-distance chromatic number of trees and cyclesNiranjan P.K.0Srinivasa Rao Kola1Corresponding author.; Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Surathkal, IndiaDepartment of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Surathkal, IndiaFor any positive integer k, a k-distance coloring of a graph G is a vertex coloring of G in which no two vertices at distance less than or equal to k receive the same color. The k-distance chromatic number of G, denoted by χkGis the smallest integer α for which G has a k-distance α-coloring. In this paper, we improve the lower bound for the k-distance chromatic number of an arbitrary graph for k odd case and see that trees achieve this lower bound by determining the k-distance chromatic number of trees. Also, we find k-distance chromatic number of cycles and 2-distance chromatic number of a graph G in which every pair of cycles are edge disjoint. Keywords: Distance coloring, k-distance chromatic number, 2-distance chromatic numberhttp://www.sciencedirect.com/science/article/pii/S0972860017301056
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Niranjan P.K. Srinivasa Rao Kola
spellingShingle	Niranjan P.K. Srinivasa Rao Kola The k-distance chromatic number of trees and cycles AKCE International Journal of Graphs and Combinatorics
author_facet	Niranjan P.K. Srinivasa Rao Kola
author_sort	Niranjan P.K.
title	The k-distance chromatic number of trees and cycles
title_short	The k-distance chromatic number of trees and cycles
title_full	The k-distance chromatic number of trees and cycles
title_fullStr	The k-distance chromatic number of trees and cycles
title_full_unstemmed	The k-distance chromatic number of trees and cycles
title_sort	k-distance chromatic number of trees and cycles
publisher	Taylor & Francis Group
series	AKCE International Journal of Graphs and Combinatorics
issn	0972-8600
publishDate	2019-08-01
description	For any positive integer k, a k-distance coloring of a graph G is a vertex coloring of G in which no two vertices at distance less than or equal to k receive the same color. The k-distance chromatic number of G, denoted by χkGis the smallest integer α for which G has a k-distance α-coloring. In this paper, we improve the lower bound for the k-distance chromatic number of an arbitrary graph for k odd case and see that trees achieve this lower bound by determining the k-distance chromatic number of trees. Also, we find k-distance chromatic number of cycles and 2-distance chromatic number of a graph G in which every pair of cycles are edge disjoint. Keywords: Distance coloring, k-distance chromatic number, 2-distance chromatic number
url	http://www.sciencedirect.com/science/article/pii/S0972860017301056
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The k-distance chromatic number of trees and cycles

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