Extremal values for ratios of distances in trees
The authors study the distance parameters of a connected graph \(G\): \[ \sigma(u):=\sum_{v\in V(G)}d(u,v) \quad\text{and}\quad \sigma(G):=\frac 12\sum_{u\in V(G)}\sigma(u), \] in the case of trees. Extremal values for the ratios \(\sigma(T)/ \sigma(v)\), \(\sigma(T)/\sigma(w)\), \(\sigma(w)/\sigma(v)\), and \(\sigma(w)/\sigma(u)\) are determined, where \(T\) is a tree of order \(n\), \(v\) is a centroid vertex of \(T\), and \(w\) and \(u\) are end vertices of \(T\).
scientific article; zbMATH DE number 1109899