Graphs with least eigenvalue -2: A new proof of the 31 forbidden subgraphs theorem

Citation

Cvetkovic D, Rowlinson P & Simic S (2005) Graphs with least eigenvalue -2: A new proof of the 31 forbidden subgraphs theorem. Designs, Codes and Cryptography, 34 (2-3), pp. 229-240. https://doi.org/10.1007/s10623-004-4856-5

Abstract
Generalized line graphs were introduced by Hoffman Proc. Calgary Internat. Conf. on Combinatorial Structures and their applications, Gordon and Breach, New York (1970); they were characterized in 1980 by a collection of 31 forbidden induced subgraphs, obtained independently by Cvetković et al., Comptes Rendus Math. Rep. Acad. Sci. Canada (1980) and S. B. Rao et al., Proc. Second Symp., Indian Statistical Institute, Calcutta, Lecture Notes in Math., (1981). Here a short new proof of this characterization theorem is given, based on an edge-colouring technique.

Keywords
graph spectra; least eigenvalue; generalized line graphs; forbidden subgraphs

Journal
Designs, Codes and Cryptography: Volume 34, Issue 2-3

People

Professor Peter Rowlinson

Emeritus Professor, Mathematics