Complete the characterization of intermediate local metric dimensions

Complete the characterization of graphs with intermediate values of local metric dimension ldim(G) and fault-tolerant local metric dimension ftldim(G), beyond the cases ldim(G) ∈ {0,1} and the corresponding extremal cases ftldim(G) ∈ {1,2,n}.

Background

The paper gives characterizations for the minimum and maximum values of local metric dimension and fault-tolerant local metric dimension. The authors explicitly identify the remaining task of describing graphs attaining other values.