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Line graphs of bipartite graphs with Hamiltonian paths

✍ Scribed by Francis K. Bell

Publisher: John Wiley and Sons
Year: 2003
Tongue: English
Weight: 115 KB
Volume: 43
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.10107

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✦ Synopsis

It is shown that, if t is an integer !3 and not equal to 7 or 8, then there is a unique maximal graph having the path P t as a star complement for the eigenvalue À2: The maximal graph is the line graph of K m,m if t ¼ 2mÀ1, and of K m,m þ1 if t ¼ 2m. This result yields a characterization of L(G ) when G is a ðt þ 1Þ-vertex bipartite graph with a Hamiltonian path. The graphs with star complement P r [ P s or P r [ C s for À2 are also determined.

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