|Appears in Collections:||Computing Science and Mathematics Journal Articles|
|Peer Review Status:||Refereed|
|Title:||Star complements and exceptional graphs|
Simic, Slobodan K
|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.|
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