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 Algebra Discrete Math.: Year: Volume: Issue: Page: Find

 Algebra Discrete Math., 2018, Volume 26, Issue 2, Pages 256–269 (Mi adm682)

RESEARCH ARTICLE

On unicyclic graphs of metric dimension 2 with vertices of degree 4

M. Dudenko, B. Oliynyk

Department of Mathematics, National University of Kyiv-Mohyla Academy, Skovorody St. 2, Kyiv, 04070, Ukraine

Abstract: We show that if $G$ is a unicyclic graph with metric dimension $2$ and $\{a,b\}$ is a metric basis of $G$ then the degree of any vertex $v$ of $G$ is at most $4$ and degrees of both $a$ and $b$ are at most $2$. The constructions of unispider and semiunispider graphs and their knittings are introduced. Using these constructions all unicyclic graphs of metric dimension $2$ with vertices of degree $4$ are characterized.

Keywords: graph, distance, metric dimension, unicyclic graph.

 Funding Agency Grant Number Charitable Foundation for Renaissance of the Kyiv-Mohyla Academy The authors thank to the International Charitable Foundation for Renaissance of the Kyiv-Mohyla Academy for the financial support of their research.

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MSC: 05C12
Revised: 18.12.2018
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Citation: M. Dudenko, B. Oliynyk, “On unicyclic graphs of metric dimension 2 with vertices of degree 4”, Algebra Discrete Math., 26:2 (2018), 256–269

Citation in format AMSBIB
\Bibitem{DudOli18} \by M.~Dudenko, B.~Oliynyk \paper On unicyclic graphs of metric dimension~2 with vertices of degree~4 \jour Algebra Discrete Math. \yr 2018 \vol 26 \issue 2 \pages 256--269 \mathnet{http://mi.mathnet.ru/adm682}