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The partition dimension of the vertex amalgamation of some cycles

Let [Formula: see text] be a connected, finite, simple, and undirected graph. The distance between two vertices [Formula: see text] , denoted by [Formula: see text] , is the shortest length of [Formula: see text]-path in G. The distance between a vertex [Formula: see text] is defined as [Formula: se...

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Autores principales: Hasmawati, Hinding, Nurdin, Nurwahyu, Budi, Syukur Daming, Ahmad, Kamal Amir, Amir
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Elsevier 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9193875/
https://www.ncbi.nlm.nih.gov/pubmed/35711982
http://dx.doi.org/10.1016/j.heliyon.2022.e09596
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author Hasmawati
Hinding, Nurdin
Nurwahyu, Budi
Syukur Daming, Ahmad
Kamal Amir, Amir
author_facet Hasmawati
Hinding, Nurdin
Nurwahyu, Budi
Syukur Daming, Ahmad
Kamal Amir, Amir
author_sort Hasmawati
collection PubMed
description Let [Formula: see text] be a connected, finite, simple, and undirected graph. The distance between two vertices [Formula: see text] , denoted by [Formula: see text] , is the shortest length of [Formula: see text]-path in G. The distance between a vertex [Formula: see text] is defined as [Formula: see text] where [Formula: see text] , denoted by [Formula: see text]. For an ordered partition [Formula: see text] of the vertices of a graph G, the partition representation of a vertex [Formula: see text] with respect to Π is defined as the k-vektor [Formula: see text]. The partition set Π is called a resolving partition of G, if [Formula: see text] , for all [Formula: see text] , [Formula: see text]. The partition dimension of G is the minimum number of sets in any resolving partition of G. In this paper we study the partition dimension of the vertex amalgamation of some cycles. Specifically, we present the vertex amalgamation of m copies of the cycle [Formula: see text] at a fixed vertex [Formula: see text] , for [Formula: see text] and [Formula: see text] , [Formula: see text].
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spelling pubmed-91938752022-06-15 The partition dimension of the vertex amalgamation of some cycles Hasmawati Hinding, Nurdin Nurwahyu, Budi Syukur Daming, Ahmad Kamal Amir, Amir Heliyon Research Article Let [Formula: see text] be a connected, finite, simple, and undirected graph. The distance between two vertices [Formula: see text] , denoted by [Formula: see text] , is the shortest length of [Formula: see text]-path in G. The distance between a vertex [Formula: see text] is defined as [Formula: see text] where [Formula: see text] , denoted by [Formula: see text]. For an ordered partition [Formula: see text] of the vertices of a graph G, the partition representation of a vertex [Formula: see text] with respect to Π is defined as the k-vektor [Formula: see text]. The partition set Π is called a resolving partition of G, if [Formula: see text] , for all [Formula: see text] , [Formula: see text]. The partition dimension of G is the minimum number of sets in any resolving partition of G. In this paper we study the partition dimension of the vertex amalgamation of some cycles. Specifically, we present the vertex amalgamation of m copies of the cycle [Formula: see text] at a fixed vertex [Formula: see text] , for [Formula: see text] and [Formula: see text] , [Formula: see text]. Elsevier 2022-05-31 /pmc/articles/PMC9193875/ /pubmed/35711982 http://dx.doi.org/10.1016/j.heliyon.2022.e09596 Text en © 2022 The Authors https://creativecommons.org/licenses/by-nc-nd/4.0/This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
spellingShingle Research Article
Hasmawati
Hinding, Nurdin
Nurwahyu, Budi
Syukur Daming, Ahmad
Kamal Amir, Amir
The partition dimension of the vertex amalgamation of some cycles
title The partition dimension of the vertex amalgamation of some cycles
title_full The partition dimension of the vertex amalgamation of some cycles
title_fullStr The partition dimension of the vertex amalgamation of some cycles
title_full_unstemmed The partition dimension of the vertex amalgamation of some cycles
title_short The partition dimension of the vertex amalgamation of some cycles
title_sort partition dimension of the vertex amalgamation of some cycles
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9193875/
https://www.ncbi.nlm.nih.gov/pubmed/35711982
http://dx.doi.org/10.1016/j.heliyon.2022.e09596
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