On graphs with complete bipartite star complements Original Research Article

Let μ be an eigenvalue of the graph G with multiplicity m. A star complement for μ in G is an induced subgraph G−X such that midXmid=m and μ is not an eigenvalue of G−X. Some general observations concerning graphs with the complete bipartite graph Kr,s(r+s>2) as a star complement are followed by a complete analysis of the case r=2, s=5. The results include a characterization of the Schläfli graph and the construction of all the regular graphs which have K2,5 as a star complement.