On unicyclic graphs of metric dimension \(2\)

Margaryta Dudenko, Bogdana Oliynyk


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.


distance, metric dimensions, unicyclic graph

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