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Algebra and Discrete Mathematics, 2017, Volume 23, Issue 2, Pages 216–222 (Mi adm604)  

This article is cited in 2 scientific papers (total in 2 papers)

RESEARCH ARTICLE

On unicyclic graphs of metric dimension $2$

Marharyta Dudenko, Bogdana Oliynyk

Department of Mathematics, National University of Kyiv-Mohyla Academy, Skovorody St. 2, Kyiv, 04070, Ukraine
Full-text PDF (282 kB) Citations (2)
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Abstract: A metric basis $S$ of a graph $G$ is the subset of vertices of minimum cardinality such that all other vertices are uniquely determined by their distances to the vertices in $S$. The metric dimension of a graph $G$ is the cardinality of the subset $S$. A unicyclic graph is a graph containing exactly one cycle. The construction of a knitting unicyclic graph is introduced. Using this construction all unicyclic graphs with two main vertices and metric dimensions $2$ are characterized.
Keywords: distance, metric dimensions, unicyclic graph.
Received: 08.06.2017
Revised: 10.06.2017
Bibliographic databases:
Document Type: Article
MSC: 05C12
Language: English
Citation: Marharyta Dudenko, Bogdana Oliynyk, “On unicyclic graphs of metric dimension $2$”, Algebra Discrete Math., 23:2 (2017), 216–222
Citation in format AMSBIB
\Bibitem{DudOli17}
\by Marharyta~Dudenko, Bogdana~Oliynyk
\paper On unicyclic graphs of metric dimension~$2$
\jour Algebra Discrete Math.
\yr 2017
\vol 23
\issue 2
\pages 216--222
\mathnet{http://mi.mathnet.ru/adm604}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000406416100004}
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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Algebra and Discrete Mathematics
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    Full-text PDF :152
    References:32
     
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