HL-index of a graph

Abstract

Let G be a simple, connected graph with n vertices and eigenvalues λ1 > λ2 ≥ λn. If n is even, define H = n/2 and L = H +1. If n is odd, define H = L = (n+1)=2. Define the HL-index of G to be R(G) = max(λH| |λ|). The eigenvalues |λH| and |λL| appear in chemical graph theory in the study of molecular stability. In this paper, bounds on HL-index for chemical and general graphs are studied. It is shown that there exist graphs with arbitrarily large HL-index. Copyright © 2012 DMFA Slovenije.