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Algebra and Discrete Mathematics, 2017, Volume 23, Issue 2, Pages 216–222
(Mi adm604)
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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
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
Citation:
Marharyta Dudenko, Bogdana Oliynyk, “On unicyclic graphs of metric dimension $2$”, Algebra Discrete Math., 23:2 (2017), 216–222
Linking options:
https://www.mathnet.ru/eng/adm604 https://www.mathnet.ru/eng/adm/v23/i2/p216
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Abstract page: | 215 | Full-text PDF : | 152 | References: | 32 |
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