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Algebra and Discrete Mathematics, 2018, Volume 26, Issue 2, Pages 256–269
(Mi adm682)
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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.
Received: 14.10.2018 Revised: 18.12.2018
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
Linking options:
https://www.mathnet.ru/eng/adm682 https://www.mathnet.ru/eng/adm/v26/i2/p256
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Abstract page: | 156 | Full-text PDF : | 39 | References: | 31 |
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