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.

Keywords:

• Network
• polymer
• degree profile
• depth
• diameter

AMS subject classifications:

• Primary: 05082
• 05C12
• 90B15
• Secondary: 60C05

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Polymer graphs is only a name for the class of graphs we deal with. We make no claim that chemical compounds follow this model of randomness, though some follow the method of hooking described.