On graphs whose least eigenvalue is greater than -2

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...

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Published inLinear & multilinear algebra Vol. 64; no. 8; pp. 1570 - 1582
Main Authors Belardo, Francesco, Pisanski, Tomaž, Simić, Slobodan K.
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 02.08.2016
Taylor & Francis Ltd
Subjects
adjacency matrix
Eigenvalues
Graph theory
Graphs
HOMO-LUMO
Invariants
least eigenvalue
line graph
Linear algebra
Presses
signed graph
Spectra
subdivision graph
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Summary: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.
Bibliography:ObjectType-Article-1
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ISSN:0308-1087
1563-5139
DOI:10.1080/03081087.2015.1107020