Graphs with least eigenvalue \(-2\); a historical survey and recent developments in maximal exceptional graphs
Connected graphs with least eigenvalue at least \(-2\) are either generalized line graphs or so-called exceptional graphs. The author surveys a variety of results in the study of these graphs and reports on the recent characterization of all (maximal) exceptional graphs independently accomplished by two groups of researchers one of which containing him. The basic techniques used for this characterization are the use of representations of the graphs using root systems known from the theory of Lie algebras and the so-called star complement technique. The author sketches a proof that all exceptional graphs, except for the cone over \(L(K_8)\), can be obtained by the star complement technique from a unique (exceptional) star complement for the eigenvalue \(-2\).
scientific article; zbMATH DE number 1864761
scientific article