Abstract
In the 1970s two different structure-descriptors were put forward, aimed at quantifying the extent of branching of the carbon-atom skeleton of organic molecules: Randic's connectivity index, χ=∑(δrδ2)−1/2, where δr is the degree of the vertex r of the molecular graph and where the summation goes over all pairs of adjacent vertices (1975), and the greatest eigenvalue, λ1, of the molecular graph (1973, 1977). Curiously, these two branching indices were never compared. By studying the relation between λ1 and an auxiliary quantity ρ=∑(δrδ2)+1/2, as well as the relation between ρ and χ, we establish the actual relation between χ and λ1. For differently branched isomers, there is a (rough) decreasing correlation between λ1 and χ; however, within groups of similarly branched isomers the correlation between λ1 and χ increases and is nearly linear.
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