Xueliang Li, Ivan Gutman: Mathematical Aspects of Randić-type Molecular Structure Descriptors

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ON THE SUM-CONNECTIVITY INDEX (2011, background): “Its mathematical properties [9, 10] and generalizations/variants [11–13] have also been studied extensively.”
Vertex-Degree-Based Topological Indices Over Graphs (2014, methodology): “As an application of our results, we find the extremal values of the general Randić index Rt over Gn, when t belongs to the interval ( −1,−(1) 2 ) , an open problem proposed in ([12],[13]).”
Randic Matrix and Randic Energy (2010, background): “We mention in passing that the expression ∑ i∼j 1/(di dj) , equal to the half of tr(R (2)) , is just a special case of the general Randić index Rα = ∑ i∼j (di dj) α for α = −1 ; for details see [4].”
Three New/Old Vertex-Degree-Based Topological Indices (2014, background): “For a connected graph G with n vertices, R(G) ≤ n/2, with equality if and only if G is regular [15,28].”
Survey on Geometric-Arithmetic Indices of Graphs (2011, background): “There are more than thousand papers and a couple of books dealing with this molecular descriptor (for example see [41, 67, 68] and the references cited therein).”
A Survey on the Randic Index (2008, background): “For a comprehensive survey of its mathematical properties, see the book of Li and Gutman “Mathematical Aspects of Randić-Type Molecular Structure Descriptors” [48].”