Fat Hoffman graphs with smallest eigenvalue at least −1 − τ

Akihiro Munemasa, Yoshio Sano, Tetsuji Taniguchi

Abstract


In this paper, we show that all fat Hoffman graphs with smallest eigenvalue at least − 1 − τ, where τ is the golden ratio, can be described by a finite set of fat (− 1 − τ)-irreducible Hoffman graphs. In the terminology of Woo and Neumaier, we mean that every fat Hoffman graph with smallest eigenvalue at least − 1 − τ is an H-line graph, where H is the set of isomorphism classes of maximal fat (− 1 − τ)-irreducible Hoffman graphs. It turns out that there are 37 fat (− 1 − τ)-irreducible Hoffman graphs, up to isomorphism.


Keywords


Hoffman graph, line graph, graph eigenvalue, special graph

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DOI: https://doi.org/10.26493/1855-3974.287.137

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