Characterization of molecular branching

By M. Randic. 1975

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On the Randić Index (2005, background): “In the paper, we first point out a careless mistake in the proof of their result (Theorem 2 of [2]), and then we will show that the result holds when δ(G) ≥ 2.”
A Unified Approach to Extremal Cacti for Different Indices (2008, background): “where m(G;k) is the number of k-independent edge sets of G. Note that m(G;0) = 1. (iv) The Randi´c index of G is defined (see [ 18 ]) as”
On the Randić index and conditional parameters of a graph (2013, background): “The Wiener index W (Γ) of a graph Γ with vertex set {v1, v2, ..., vn} defined as the sum of distances between all pairs of vertices of Γ, W (Γ) := 1 2 n ∑ i=1,j=1 ∂(vi, vj), is the first mathematical invariant reflecting the topological structure of a molecular graph.”
The Use of Topological Indices in QSAR and QSPR Modeling (2017, methodology): “Randić (1975) devised a topological index to characterize branching in alkanes.”
Vertex-Degree-Based Topological Indices Over Graphs (2014, methodology): “One of the most widely used topological indices in applications to physical and chemical properties is the Randić index [16], which is defined for a graph G as”