Skip header navigation
×

Article

Star complements and exceptional graphs

Citation
Cvetkovic D, Rowlinson P & Simic SK (2007) Star complements and exceptional graphs. Linear Algebra and Its Applications, 423 (1), pp. 146-154. https://doi.org/10.1016/j.laa.2007.01.008

Abstract
Let G be a finite graph of order n with an eigenvalue ? of multiplicity k. (Thus the ?-eigenspace of a (0,1)-adjacency matrix of G has dimension k.) A star complement for ? in G is an induced subgraph G-X of G such that |X|=k and G-X does not have ? as an eigenvalue. An exceptional graph is a connected graph, other than a generalized line graph, whose eigenvalues lie in [-2,?). We establish some properties of star complements, and of eigenvectors, of exceptional graphs with least eigenvalue -2.

Keywords
Graph; Eigenvalue; Star complement

Journal
Linear Algebra and Its Applications: Volume 423, Issue 1

StatusPublished
Author(s)Cvetkovic, Dragos; Rowlinson, Peter; Simic, Slobodan K
Publication date31/05/2007
Publication date online20/01/2007
URLhttp://hdl.handle.net/1893/18451
PublisherElsevier
ISSN0024-3795
Scroll back to the top