Maximal Lanzhou index of trees and unicyclic graphs with prescribed diameter

Given a connected graph G, its Lanzhou index is Lz(G)=∑v∈V(G)d(v)2[n−1−d(v)], where n is the order and d(v) is the degree of v∈G. As usual with topological indices and their meaning in Chemical Graph Theory, we are interested in determining the graphs maximizing or minimizing the considered index. We show that by applying the majorization method, we identify all unified extremal trees with maximum Lanzhou index among the trees of order n and diameter d≥8. Using the same method, we identify the unified extremal unicyclic graphs with maximum Lanzhou index among the unicyclic graphs of order n and diameter d≥9 with n≥3d−8.