Choosing the exponent in the definition of the connectivity index

Abstract

Let du denote the degree of the vertex u of a molecular graph G. Then the connectivity index of G is defined as C (l) = G (l; C) = S (dudu)l, where the summation goes over all pairs of adjacent vertices. The exponent l is usually chosen to be equal to –1/2, but other options were considered as well, especially l = –1. We show that whereas C(–1/2) is a suitable measure of branching of the carbon-atom skeleton of organic molecules, and thus applicable as a topological index for modeling physico-chemical properties of the respective compounds, this is not the case with C(–1). The value of l is established, beyond which C(l) fails to correctly reflect molecular branching.

Keywords

• connectivity index
• branching
• topological index
• tree
• chemical tree