Lanzhou Index of Trees and Unicyclic Graphs

Abstract

Let G be a simple graph with vertex set V (G).The Lanzhou index of G is defined as Lz(G) = u∈V (G) d G (u)dG(u) 2 , where dG(u) denotes the degree of the vertex u in G and G is the complement of G.In this paper, we establish an upper bound on the Lanzhou index for trees of order n with maximum degree ∆.Additionally, we obtain the minimum and maximum values of the Lanzhou index for unicyclic graphs of order n.Moreover, we determine the Lanzhou index's maximum value for chemical trees of order n.