On unicyclic graphs of metric dimension $2$

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.