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On graphs with complete bipartite star complements

✍ Scribed by P.S. Jackson; P. Rowlinson

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 119 KB
Volume: 298
Category: Article
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(99)00135-4

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✦ Synopsis

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 K r,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 K 2,5 as a star complement.

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