On graphs with the smallest eigenvalue at least −1 − √2, part III

Sho Kubota, Tetsuji Taniguchi, Kiyoto Yoshino

Abstract


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.


Keywords


Hoffman graph, line graph, smallest eigenvalue

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DOI: https://doi.org/10.26493/1855-3974.1581.b47

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications