Spectral Characterizations of Line Graphs. Variations on the Theme

Dragoš_M. Cvetković

The following three topics related to spectral characterizations of line graphs are discussed: local structure of regular graphs with the least eigenvalue $-2$ which contain $K_{1,3}$ as an induced subgraph, switching regular line graphs into regular graphs which are not line graphs, and line switching (of graphs) as a modification of familiar (vertex) switching.