A recursive construction of the regular exceptional graphs with least eigenvalue \(-2\) (Q399386)

Summary: In spectral graph theory a graph with least eigenvalue \(-2\) is exceptional if it is connected, has least eigenvalue greater than or equal to \(-2\), and it is not a generalized line graph. A \((\kappa,\tau)\)-regular set \(S\) of a graph is a vertex subset, inducing a \(\kappa\)-regular subgraph such that every vertex not in \(S\) has \(\tau\) neighbors in \(S\). We present a recursive construction of all regular exceptional graphs as successive extensions by regular sets.