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.
