Abstract
We study the phenomenon of cospectrality in generalized line graphs and in exceptional graphs. We survey old results from today's point o view and obtain some new results partly by the use of compute. Among.other things we show that a connected generalized line graph L(H) has an exceptional cospectral mate only if its root graph H, assuming it is itself connected has at most 9 vertices. The paper contains a description of a table of sets of cospectral graphs with least eigenvalue at least ?2 and at most 8 vertices together with some comments and theoretical explanations of the phenomena suggested by the table.
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