On graphs with complete bipartite star complements

Citation

Jackson P & Rowlinson P (1999) On graphs with complete bipartite star complements. Linear Algebra and Its Applications, 298 (1-3), pp. 9-20. https://doi.org/10.1016/S0024-3795%2899%2900135-4

Abstract
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 ∣X∣=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.

Keywords
graph; eigenvalue; eigenspace

Journal
Linear Algebra and Its Applications: Volume 298, Issue 1-3