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In spectral graph theory a graph with least eigenvalue is exceptional if it is connected, has least eigenvalue greater than or equal to , and it is not a generalized line graph. A -regular set of a graph is a vertex subset, inducing a -regular subgraph such that every vertex not in has neighbors in . We present a recursive construction of all regular exceptional graphs as successive extensions by regular sets.
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Inês Barbedo, Domingos M. Cardoso, Dragoš Cvetković, Paula Rama, Slobodan K. Simić, A recursive construction of the regular exceptional graphs with least eigenvalue –2. Port. Math. 71 (2014), no. 2 pp. 79–96