Exponent-dependent properties of the connectivity index
İvan Gutman, Mirko Lepović, Dušica Vidović, Lane Clark · INDIAN JOURNAL OF CHEMISTRY- SECTION A · 2002
The connectivity index is defined as C(λ) =Σ(δ u δ v ) θ , where δ v is the degree of the vertex v of the respective molecular graph, and where the summation embraces all pairs of adjacent vertices. The exponent λ is usuallychosen to be equal to -0.5 but other options have been considered as well, especially C(-1). We show that whereas C(-0.5) correctly reflects the extent of branching of the carbon-atom skeleton of organic molecules, and is thus a suitable topological index for modelling physico-chemical properties of the respective compounds, this is not the case when the exponent λ assumes larger negative values, in particular when λ=-1. The value of λ is established beyond which C(λ) fails to be a measure of molecular branching.