HL-index of a graph - Jaklič, Gašper (Ars mathematica contemporanea, 2012)
Let ?$G$? be a simple, connected graph with ?$n$? vertices and eigenvalues ?$λ_1 > λ_2 \ge … \ge λ_n$?. 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 ?$R(G) = \max(|λ_H|, |λ_L|)$?. The eigenvalues ?$λ_H$? and ?$λ_L$? 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.
Keywords: graph spectrum; graph theory; HL-indeks; HL-index; HOMO-LUMO map; HOMO-LUMO preslikava; spekter grafa; teorija grafov