On graphs whose least eigenvalue is greater than –2

Abstract

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.