Bounds on the domination number and the metric dimension of co-normal product of graphs

In this paper, we establish bounds on the domination number and the metric dimension of the co-normal product graph [Formula: see text] of two simple graphs G and H in terms of parameters associated with G and H. We also give conditions on the graphs G and H for which the domination number of [Formu...

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Detalles Bibliográficos
Autores principales: Javaid, Imran, ur Rehman, Shahid, Imran, Muhammad
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6061539/
https://www.ncbi.nlm.nih.gov/pubmed/30137890
http://dx.doi.org/10.1186/s13660-018-1752-5
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author Javaid, Imran
ur Rehman, Shahid
Imran, Muhammad
author_facet Javaid, Imran
ur Rehman, Shahid
Imran, Muhammad
author_sort Javaid, Imran
collection PubMed
description In this paper, we establish bounds on the domination number and the metric dimension of the co-normal product graph [Formula: see text] of two simple graphs G and H in terms of parameters associated with G and H. We also give conditions on the graphs G and H for which the domination number of [Formula: see text] is 1, 2, and the domination number of G. Moreover, we give formulas for the metric dimension of the co-normal product [Formula: see text] of some families of graphs G and H as a function of associated parameters of G and H.
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spelling pubmed-60615392018-08-09 Bounds on the domination number and the metric dimension of co-normal product of graphs Javaid, Imran ur Rehman, Shahid Imran, Muhammad J Inequal Appl Research In this paper, we establish bounds on the domination number and the metric dimension of the co-normal product graph [Formula: see text] of two simple graphs G and H in terms of parameters associated with G and H. We also give conditions on the graphs G and H for which the domination number of [Formula: see text] is 1, 2, and the domination number of G. Moreover, we give formulas for the metric dimension of the co-normal product [Formula: see text] of some families of graphs G and H as a function of associated parameters of G and H. Springer International Publishing 2018-07-04 2018 /pmc/articles/PMC6061539/ /pubmed/30137890 http://dx.doi.org/10.1186/s13660-018-1752-5 Text en © The Author(s) 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Javaid, Imran
ur Rehman, Shahid
Imran, Muhammad
Bounds on the domination number and the metric dimension of co-normal product of graphs
title Bounds on the domination number and the metric dimension of co-normal product of graphs
title_full Bounds on the domination number and the metric dimension of co-normal product of graphs
title_fullStr Bounds on the domination number and the metric dimension of co-normal product of graphs
title_full_unstemmed Bounds on the domination number and the metric dimension of co-normal product of graphs
title_short Bounds on the domination number and the metric dimension of co-normal product of graphs
title_sort bounds on the domination number and the metric dimension of co-normal product of graphs
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6061539/
https://www.ncbi.nlm.nih.gov/pubmed/30137890
http://dx.doi.org/10.1186/s13660-018-1752-5
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