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 ) = (cid:80) u ∈ V ( G ) d G ( u ) d G ( u ) 2 , where d G ( 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 .