Metric dimension and its variations of chain graphs

Chain graphs and threshold graphs are characterized as graphs with the largest spectral radius among all connected bipartite graphs (former one) and all connected graphs (latter one) with prescribed order and size. In this article, we derive results on the metric dimension of chain and threshold graphs. We present an algorithm which returns a chain graph (if one exists) having specified order and metric dimension. We define the restricted threshold dimension of chain graphs which minimizes the metric dimension of graphs obtained by adding edges while keeping the nesting property and bipartiteness. We also derive related results.