2014
DOI: 10.1016/j.dam.2014.01.008
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Fat Hoffman graphs with smallest eigenvalue greater than −3

Abstract: In this paper, we give a combinatorial characterization of the special graphs of fat Hoffman graphs containing K 1,2 with smallest eigenvalue greater than −3, where K 1,2 is the Hoffman graph having one slim vertex and two fat vertices.

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Cited by 4 publications
(7 citation statements)
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“…Recently, Jang, Koolen, Munemasa, and Taniguchi [14] proposed a programme to classify fat Hoffman graphs with smallest eigenvalue at least −3. The present work fills a part of this programme, and includes the results of [17].…”
Section: Introductionmentioning
confidence: 93%
See 2 more Smart Citations
“…Recently, Jang, Koolen, Munemasa, and Taniguchi [14] proposed a programme to classify fat Hoffman graphs with smallest eigenvalue at least −3. The present work fills a part of this programme, and includes the results of [17].…”
Section: Introductionmentioning
confidence: 93%
“…A Hoffman graph H is defined as a graph (V, E) with a distinguished coclique V f (H) ⊂ V called fat vertices, the remaining vertices V s (H) = V \V f (H) are called slim vertices. For more background on Hoffman graphs see some of the authors' previous papers [14,16,17]. Let H be a Hoffman graph and suppose its adjacency matrix A has the following form…”
Section: Hoffman Graphsmentioning
confidence: 99%
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“…Recently Greaves et al [53] proved Hoffman's conjecture (with an extension to signed graphs); another proof is given in [79]. This effectively deals with limit points greater than −2.…”
Section: Theorem 81 the Real Number σ Is A Limit Point Greater Thanmentioning
confidence: 99%
“…When the fat indecomposable Hoffman graph H has a vertex with exactly two fat neighbours, necessary and sufficient structural conditions for λ(H) > −3 are known from [79,Theorem 4.3]. One consequence is the following result, which should be compared with Theorem 8.1.…”
Section: Theorem 81 the Real Number σ Is A Limit Point Greater Thanmentioning
confidence: 99%