Independent point-set domination in line graphs

Line graph of a graph G is an intersection graph of the edge set E(G) of G. In this paper, we obtain a sharp upper bound on the diameter of graph G whose line graph is an ipsd graph (graph possessing an independent point-set dominating set) by establishing a fundamental relation between diameter of...

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Autores principales:	Purnima Gupta, Alka Goyal, Ranjana Jain
Formato:	article
Lenguaje:	EN
Publicado:	Taylor & Francis Group 2021
Materias:	domination point-set domination independent set line graph Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/b92e3f8397bb4782a9662d610615280e
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id	oai:doaj.org-article:b92e3f8397bb4782a9662d610615280e
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spelling	oai:doaj.org-article:b92e3f8397bb4782a9662d610615280e2021-11-11T14:23:41ZIndependent point-set domination in line graphs0972-86002543-347410.1080/09728600.2021.1995307https://doaj.org/article/b92e3f8397bb4782a9662d610615280e2021-10-01T00:00:00Zhttp://dx.doi.org/10.1080/09728600.2021.1995307https://doaj.org/toc/0972-8600https://doaj.org/toc/2543-3474Line graph of a graph G is an intersection graph of the edge set E(G) of G. In this paper, we obtain a sharp upper bound on the diameter of graph G whose line graph is an ipsd graph (graph possessing an independent point-set dominating set) by establishing a fundamental relation between diameter of G and diameter of its line graph L(G). We prove that if for a graph G, the length of the longest induced cycle is greater than 5, then its line graph does not possess an ipsd-set. Further we characterize certain classes of graphs viz., trees, complete graphs and complete bipartite graphs whose line graphs possess an independent point set dominating set.Purnima GuptaAlka GoyalRanjana JainTaylor & Francis Grouparticledominationpoint-set dominationindependent setline graphMathematicsQA1-939ENAKCE International Journal of Graphs and Combinatorics, Vol 0, Iss 0, Pp 1-6 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	domination point-set domination independent set line graph Mathematics QA1-939
spellingShingle	domination point-set domination independent set line graph Mathematics QA1-939 Purnima Gupta Alka Goyal Ranjana Jain Independent point-set domination in line graphs
description	Line graph of a graph G is an intersection graph of the edge set E(G) of G. In this paper, we obtain a sharp upper bound on the diameter of graph G whose line graph is an ipsd graph (graph possessing an independent point-set dominating set) by establishing a fundamental relation between diameter of G and diameter of its line graph L(G). We prove that if for a graph G, the length of the longest induced cycle is greater than 5, then its line graph does not possess an ipsd-set. Further we characterize certain classes of graphs viz., trees, complete graphs and complete bipartite graphs whose line graphs possess an independent point set dominating set.
format	article
author	Purnima Gupta Alka Goyal Ranjana Jain
author_facet	Purnima Gupta Alka Goyal Ranjana Jain
author_sort	Purnima Gupta
title	Independent point-set domination in line graphs
title_short	Independent point-set domination in line graphs
title_full	Independent point-set domination in line graphs
title_fullStr	Independent point-set domination in line graphs
title_full_unstemmed	Independent point-set domination in line graphs
title_sort	independent point-set domination in line graphs
publisher	Taylor & Francis Group
publishDate	2021
url	https://doaj.org/article/b92e3f8397bb4782a9662d610615280e
work_keys_str_mv	AT purnimagupta independentpointsetdominationinlinegraphs AT alkagoyal independentpointsetdominationinlinegraphs AT ranjanajain independentpointsetdominationinlinegraphs
_version_	1718438979563421696

Independent point-set domination in line graphs

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