Existence of independent [1, 2]-sets in caterpillars

Given a graph G, a subset S ⊆ V (G) is an independent [1, 2]-set if no two vertices in S are adjacent and for every vertex ν ∈ V (G)\S, 1 ≤ |N(ν) ∩ S| ≤ 2, that is, every vertex ν ∈ V (G)\S is adjacent to at least one but not more than two vertices in S. In this paper, we discuss the existence of in...

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Main Authors:	Santoso, Eko Budi, Marcelo, Reginaldo M
Format:	text
Published:	Archīum Ateneo 2016
Subjects:	Number Theory
Online Access:	https://archium.ateneo.edu/mathematics-faculty-pubs/79 https://aip.scitation.org/doi/abs/10.1063/1.4940820
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Institution:	Ateneo De Manila University

id	ph-ateneo-arc.mathematics-faculty-pubs-1078
record_format	eprints
spelling	ph-ateneo-arc.mathematics-faculty-pubs-10782020-06-04T07:11:33Z Existence of independent [1, 2]-sets in caterpillars Santoso, Eko Budi Marcelo, Reginaldo M Given a graph G, a subset S ⊆ V (G) is an independent [1, 2]-set if no two vertices in S are adjacent and for every vertex ν ∈ V (G)\S, 1 ≤ \|N(ν) ∩ S\| ≤ 2, that is, every vertex ν ∈ V (G)\S is adjacent to at least one but not more than two vertices in S. In this paper, we discuss the existence of independent [1, 2]-sets in a family of trees called caterpillars. 2016-01-01T08:00:00Z text https://archium.ateneo.edu/mathematics-faculty-pubs/79 https://aip.scitation.org/doi/abs/10.1063/1.4940820 Mathematics Faculty Publications Archīum Ateneo Number Theory
institution	Ateneo De Manila University
building	Ateneo De Manila University Library
country	Philippines
collection	archium.Ateneo Institutional Repository
topic	Number Theory
spellingShingle	Number Theory Santoso, Eko Budi Marcelo, Reginaldo M Existence of independent [1, 2]-sets in caterpillars
description	Given a graph G, a subset S ⊆ V (G) is an independent [1, 2]-set if no two vertices in S are adjacent and for every vertex ν ∈ V (G)\S, 1 ≤ \|N(ν) ∩ S\| ≤ 2, that is, every vertex ν ∈ V (G)\S is adjacent to at least one but not more than two vertices in S. In this paper, we discuss the existence of independent [1, 2]-sets in a family of trees called caterpillars.
format	text
author	Santoso, Eko Budi Marcelo, Reginaldo M
author_facet	Santoso, Eko Budi Marcelo, Reginaldo M
author_sort	Santoso, Eko Budi
title	Existence of independent [1, 2]-sets in caterpillars
title_short	Existence of independent [1, 2]-sets in caterpillars
title_full	Existence of independent [1, 2]-sets in caterpillars
title_fullStr	Existence of independent [1, 2]-sets in caterpillars
title_full_unstemmed	Existence of independent [1, 2]-sets in caterpillars
title_sort	existence of independent [1, 2]-sets in caterpillars
publisher	Archīum Ateneo
publishDate	2016
url	https://archium.ateneo.edu/mathematics-faculty-pubs/79 https://aip.scitation.org/doi/abs/10.1063/1.4940820
_version_	1681506643290882048

Existence of independent [1, 2]-sets in caterpillars

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