Average measures in polymer graphs

Abstract

We introduce polymer graphs, a class of fast-growing networks endowed with a designated hook. We study the structure of these polymer graphs by investigating numerous average measures such as the average number of nodes of the smallest degree, the average depth of a randomly chosen node, the average degree in the graph, the average order of the sub-polymer graphs hooked into the nodes, the average eccentricity of nodes, and the average diameter of the polymer graph. The construction of polymer graphs presented here relates to the step-growth polymerization.