The local antimagic on disjoint union of some family graphs

A graph in this paper is nontrivial, finite, connected, simple, and undirected. Graph consists of a vertex set and edge set. Let u,v be two elements in vertex set, and q is the cardinality of edge set in G, a bijective function from the edge set to the first q natural number is called a vertex loc...

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Autores principales:	Marsidi Marsidi, Ika Hesti Agustin
Formato:	article
Lenguaje:	EN
Publicado:	Department of Mathematics, UIN Sunan Ampel Surabaya 2019
Materias:	local antimagic labelling; local antimagic chromatic number, disjoint union graphs Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/83cde247e475429c8a88461f633a9638
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spelling	oai:doaj.org-article:83cde247e475429c8a88461f633a96382021-12-02T14:27:12ZThe local antimagic on disjoint union of some family graphs2527-31592527-316710.15642/mantik.2019.5.2.69-75https://doaj.org/article/83cde247e475429c8a88461f633a96382019-10-01T00:00:00Zhttp://jurnalsaintek.uinsby.ac.id/index.php/mantik/article/view/647https://doaj.org/toc/2527-3159https://doaj.org/toc/2527-3167A graph in this paper is nontrivial, finite, connected, simple, and undirected. Graph consists of a vertex set and edge set. Let u,v be two elements in vertex set, and q is the cardinality of edge set in G, a bijective function from the edge set to the first q natural number is called a vertex local antimagic edge labelling if for any two adjacent vertices and , the weight of is not equal with the weight of , where the weight of (denoted by ) is the sum of labels of edges that are incident to . Furthermore, any vertex local antimagic edge labelling induces a proper vertex colouring on where is the colour on the vertex . The vertex local antimagic chromatic number is the minimum number of colours taken over all colourings induced by vertex local antimagic edge labelling of . In this paper, we discuss about the vertex local antimagic chromatic number on disjoint union of some family graphs, namely path, cycle, star, and friendship, and also determine the lower bound of vertex local antimagic chromatic number of disjoint union graphs. The chromatic numbers of disjoint union graph in this paper attend the lower bound.Marsidi MarsidiIka Hesti AgustinDepartment of Mathematics, UIN Sunan Ampel Surabayaarticlelocal antimagic labelling; local antimagic chromatic number, disjoint union graphsMathematicsQA1-939ENMantik: Jurnal Matematika, Vol 5, Iss 2, Pp 69-75 (2019)
institution	DOAJ
collection	DOAJ
language	EN
topic	local antimagic labelling; local antimagic chromatic number, disjoint union graphs Mathematics QA1-939
spellingShingle	local antimagic labelling; local antimagic chromatic number, disjoint union graphs Mathematics QA1-939 Marsidi Marsidi Ika Hesti Agustin The local antimagic on disjoint union of some family graphs
description	A graph in this paper is nontrivial, finite, connected, simple, and undirected. Graph consists of a vertex set and edge set. Let u,v be two elements in vertex set, and q is the cardinality of edge set in G, a bijective function from the edge set to the first q natural number is called a vertex local antimagic edge labelling if for any two adjacent vertices and , the weight of is not equal with the weight of , where the weight of (denoted by ) is the sum of labels of edges that are incident to . Furthermore, any vertex local antimagic edge labelling induces a proper vertex colouring on where is the colour on the vertex . The vertex local antimagic chromatic number is the minimum number of colours taken over all colourings induced by vertex local antimagic edge labelling of . In this paper, we discuss about the vertex local antimagic chromatic number on disjoint union of some family graphs, namely path, cycle, star, and friendship, and also determine the lower bound of vertex local antimagic chromatic number of disjoint union graphs. The chromatic numbers of disjoint union graph in this paper attend the lower bound.
format	article
author	Marsidi Marsidi Ika Hesti Agustin
author_facet	Marsidi Marsidi Ika Hesti Agustin
author_sort	Marsidi Marsidi
title	The local antimagic on disjoint union of some family graphs
title_short	The local antimagic on disjoint union of some family graphs
title_full	The local antimagic on disjoint union of some family graphs
title_fullStr	The local antimagic on disjoint union of some family graphs
title_full_unstemmed	The local antimagic on disjoint union of some family graphs
title_sort	local antimagic on disjoint union of some family graphs
publisher	Department of Mathematics, UIN Sunan Ampel Surabaya
publishDate	2019
url	https://doaj.org/article/83cde247e475429c8a88461f633a9638
work_keys_str_mv	AT marsidimarsidi thelocalantimagicondisjointunionofsomefamilygraphs AT ikahestiagustin thelocalantimagicondisjointunionofsomefamilygraphs AT marsidimarsidi localantimagicondisjointunionofsomefamilygraphs AT ikahestiagustin localantimagicondisjointunionofsomefamilygraphs
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The local antimagic on disjoint union of some family graphs

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