Graphs with eigenvalues at least −2

Kumar, V. Pradeep; Rao, S. B.; Singhi, N. M.

doi:10.1016/0024-3795(82)90023-4

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2022

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Cited by 12 publications

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“…Minimal forbidden graphs for the property of having least eigenvalue −2 have been found in [18] and [3]. These forbidden graphs have at most 10 vertices and there are 1812 of them.…”

Section: Below)mentioning

confidence: 98%

Graphs With Least Eigenvalue —2: A New Proof of the 31 Forbidden Subgraphs Theorem

2005

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Generalized line graphs were introduced by Hoffman Proc. Calgary Internat. Conf. on Combinatorial Structures and their applications, Gordon and Breach, New York (1970); they were characterized in 1980 by a collection of 31 forbidden induced subgraphs, obtained independently by Cvetković et al., Comptes Rendus Math. Rep. Acad. Sci. Canada (1980) and S. B. Rao et al., Proc. Second Symp., Indian Statistical Institute, Calcutta, Lecture Notes in Math., (1981). Here a short new proof of this characterization theorem is given, based on an edge-colouring technique.

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“…Minimal forbidden graphs for the property of having least eigenvalue −2 have been found in [18] and [3]. These forbidden graphs have at most 10 vertices and there are 1812 of them.…”

Section: Below)mentioning

confidence: 98%