A linear-programming approach to the generalized Randić index (Q1811120)

The sum of \((d(u)d(v))^\alpha\) over all edges \(uv\) of a graph \(G\) is called the generalized Randić index \(R_\alpha(G)\) of \(G\). The authors obtain results on graphs \(G\) with a minimum value of \(R_\alpha(G)\) among graphs with \(n\) vertices, \(m\) edges, and maximum degree at most \(\Delta\) when \(\alpha= -1/2\) or \(-1\).