Fat Hoffman graphs with smallest eigenvalue at least -1 - tau - Munemasa, Akihiro (Ars mathematica contemporanea, 2014)
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 ?$\mathcal{H}$?-line graph, where ?$\mathcal{H}$? 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: grafi; graph eigenvalue; Hoffman graph; line graph; special graph