Scaling of graphs with diameter constraint

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Abstract The effect of subgraphs gluing and cloning operations on the graph diameter is studied. A vertex-diameter graph is a graph in which all vertices belong to diametric chains. We study the possibilities of using the vertex-diameter graphs for scaling of graphs with diameter constrains. Examples of scaling of trees, fat trees, and vertex-diameter graphs via cloning and gluing operations are given. We estimate the diameter and complexity of synthesis of such graphs.