Geodesic
On unicyclic graphs of metric dimension~2 with vertices of degree~4
Algebra and discrete mathematics, Tome 26 (2018) no. 2, pp. 256-269

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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, metric dimension
Mots-clés : distance, unicyclic graph. 
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     author = {M. Dudenko and B. Oliynyk},
     title = {On unicyclic graphs of metric dimension~2 with vertices of degree~4},
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     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2018_26_2_a4/}
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M. Dudenko; B. Oliynyk. On unicyclic graphs of metric dimension~2 with vertices of degree~4. Algebra and discrete mathematics, Tome 26 (2018) no. 2, pp. 256-269. http://geodesic.mathdoc.fr/item/ADM_2018_26_2_a4/