On graphs whose least eigenvalue is greater than –2.

Graphs with least eigenvalue greater than or equal toare 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, Cambridge University Press, 2004], and the survey paper [Cvetković D, Rowlinson P, Simić S. Graphs with least eigenvalue: 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, but closest towithin 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. [ABSTRACT FROM AUTHOR]