Geodesic
On graphs with the smallest eigenvalue at least −1 − √2, part III
Ars Mathematica Contemporanea, Tome 17 (2019) no. 2, pp. 555-579.

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There are many results on graphs with the smallest eigenvalue at least −2. In order to study graphs with the eigenvalues at least −1 − √2, R. Woo and A. Neumaier introduced Hoffman graphs and ℋ-line graphs. They proved that a graph with the sufficiently large minimum degree and the smallest eigenvalue at least −1 − √2 is a slim {[h2], [h5], [h7], [h9]}-line graph. After that, T. Taniguchi researched on slim {[h2], [h5]}-line graphs. As an analogue, we reveal the condition under which a strict {[h1], [h4], [h7]}-cover of a slim {[h7]}-line graph is unique, and completely determine the minimal forbidden graphs for the slim {[h7]}-line graphs.
DOI : 10.26493/1855-3974.1581.b47
Keywords: Hoffman graph, line graph, smallest eigenvalue 
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Sho Kubota; Tetsuji Taniguchi; Kiyoto Yoshino. On graphs with the smallest eigenvalue at least −1 − √2, part III. Ars Mathematica Contemporanea, Tome 17 (2019) no. 2, pp. 555-579. doi : 10.26493/1855-3974.1581.b47. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1581.b47/

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