A KINETIC APPROACH TO THE RANDOM F-GRAPH PROCESS WITH NONUNIFORM EDGEPROBABILITIES

Starting with n labeled vertices and no edges, introduce edges, one at a time, so as to obtain a sequence of graphs each having no vertex of degree greater than f. The latter are called f-graphs. At each step t he edge to be added is selected from among those edges whose addition would not violate the f-degree restriction and with probability propor tional to the product of the respective numbers of available sites at the vertices of the potential edge. We call this procedure the Random f-Graph Process with nonunifonn edge probabilities (Rf-GP) of order n . This is in contrast to the Random f-Graph Process (Rf-GP) of order n , in which the edges that are added are selected with uniform probabil ity. Using the Law of Mass Action, chemists have derived the degree di stribution of the vertices in a graph generated by the Rf-GP. Here we apply a differential equation technique to obtain this degree distrib ution.