On graphs with complete bipartite star complements

Let mu be an eigenvalue of the graph G with multiplicity in. A star complem ent for mu in G is an induced subgraph G - X such that \X\ = m and mu is no t an eigenvalue of G - X. Some general observations concerning graphs with the complete bipartite graph K-r,K-s (r + s > 2) as a star complement are f ollowed by a complete analysis of the case r = 2, s = 5. The results includ e a characterization of the Schlafli graph and the construction of all the regular graphs which have K-2,K-5 as a star complement. (C) 1999 Published by Elsevier Science inc. All rights reserved.