METRIC DIMENSION AND ITS VARIATIONS OF CHAIN GRAPHS
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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 met- ric dimension of chain and threshold graphs. We present an algorithm which returns a chain graph (if one exists) having specifi ed order and metric dimension. We de fine 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.
Abstract
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 met- ric dimension of chain and threshold graphs. We present an algorithm which returns a chain graph (if one exists) having specifi ed order and metric dimension. We de fine 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.
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