Connected domination number, average distance and their application in drug design

Abstract

Let a graph with n vertices be G. A leaf of G is a vertex of degree 1 in G. The leaf number of G, denoted L(G), is the number of leaves in a spanning tree of G that contains the maximum number of leaves possible. The Wiener index of G, denoted W(G), is defined to be the sum of the distances between all unordered pairs of vertices in G. When the Wiener index of G, of order n, is divided by n2 , the average distance, denoted µ(G), is obtained. We are concerned with bounds on W(G) and L(G). Also, we attempt to model the biological activity of some compounds using these two Graph Theory concepts. The output of the model is analysed using statistical methods and the suitability of the parameters is determined.