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The Randić index is one of the classical graph-based molecular structure descriptors that found countless applications in chemistry and pharmacology. The mathematical background of this index is also well elaborated. We now point out a hitherto unnoticed feature of , namely its connection with the degree-based information content of a (molecular) graph. This connection is based on the linear correlation between and the logarithm of the multiplicative version of the Randić index.

Let be a finite simple undirected graph with vertices and edges. The energy of a graph , denoted by , is defined as the sum of the absolute values of the eigenvalues of . In this paper we present lower bounds for in terms of number of vertices, edges, Randić index, minimum degree, diameter, walk and determinant of the adjacency matrix. Also we show our lower bound in (11) under certain conditions is better than the classical bounds given in Caporossi et al. (1999), Das (2013) and McClelland (1971).

The general sum-connectivity index, general product-connectivity index, general Zagreb index and coindices of line graphs of subdivision graphs of tadpole graphs, wheels and ladders have been reported in the literature. In this paper, we obtain general expressions for these topological indices for the line graph of the subdivision graphs, thus generalizing the existing results.