Authors: Belardo, Francesco
Pisanski, Tomaž
Simić, Slobodan 
Title: On graphs whose least eigenvalue is greater than –2
Journal: Linear and Multilinear Algebra
Volume: 64
Issue: 8
First page: 1570
Last page: 1582
Issue Date: 2-Aug-2016
Rank: M21
ISSN: 0308-1087
DOI: 10.1080/03081087.2015.1107020
Graphs with least eigenvalue greater than or equal to -2 are to a big extent studied by Hoffman and other authors from the early beginning of the spectral graph theory. Most of these results are summarized in the monograph [Cvetković D, Rowlinson P, Simić S. Spectral generalizations of line graphs, on graphs with least eigenvalue -2 , Cambridge University Press, 2004], and the survey paper [Cvetković D, Rowlinson P, Simić S. Graphs with least eigenvalue -2 : ten years on, Linear Algebra Appl. 2015;484:504–539] which is aimed to cover the next 10 years since their monograph appeared. Here, we add some further results. Among others, we identify graphs whose least eigenvalue is greater than -2 , but closest to -2 within the graphs of fixed order. Some consequences of these considerations are found in the context of the highest occupied molecular orbital–lowest unoccupied molecular orbital invariants.
Keywords: adjacency matrix | HOMO–LUMO | least eigenvalue | line graph | signed graph | subdivision graph
Publisher: Taylor & Francis
Project: University of Primorska OP RCV_VS-13–25, the operation number 3330–14–500033
ARRS, Grant number P1-0294
Graph theory and mathematical programming with applications in chemistry and computer science 

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