On graphs whose least eigenvalue is greater than –2. Issue 8 (2nd August 2016)

• Record Type: Journal Article
• Authors: Belardo, Francesco; Pisanski, Tomaž; Simić, Slobodan K.
• Is Part Of: Linear & multilinear algebra. Volume 64:Issue 8(2016)
• Page Start: 1570
• Page End: 1582
• Publication Date: 2016-08-02
• Subjects: signed graph -- line graph -- subdivision graph -- adjacency matrix -- least eigenvalue -- HOMO–LUMO; 05C50 -- 05C90 -- 92E10; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2015.1107020
• Languages: English
• ISSNs: 0308-1087

Abstract

Abstract : Graphs with least eigenvalue greater than or equal to 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, 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 to 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.