Geodesic
HL-index of a graph
Ars Mathematica Contemporanea, Tome 5 (2012) no. 1, pp. 99-105.

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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|, |λL|). 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.
DOI : 10.26493/1855-3974.180.65e
Keywords: HL-index, graph spectrum, HOMO-LUMO map 
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Gašper Jaklič; Patrick W. Fowler; Tomaž Pisanski. HL-index of a graph. Ars Mathematica Contemporanea, Tome 5 (2012) no. 1, pp. 99-105. doi : 10.26493/1855-3974.180.65e. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.180.65e/

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