### On unicyclic graphs of metric dimension \(2\)

#### 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

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