Extremal graphs for weights
The \(\alpha\)-weight of an edge \(xy\) of a graph \(G\) is \(d(x)^\alpha\cdot d(y)^\alpha\) where \(d(x)\) and \(d(y)\) are the degrees of the vertices \(x\) and \(y\). The \(\alpha\)-weight of \(G\) is the sum of the \(\alpha\)-weights of its edges. The authors establish the \(\alpha\)-weight of a graph with any fixed number of edges for \(\alpha=1\) and determine bounds for \(\alpha\neq 1\).
scientific article; zbMATH DE number 1334436