The Gewirtz graph: An exercise in the theory of graph spectra. (English) Zbl 0794.05076

Brouwer, A. E.; Haemers, W. H.

Eur. J. Comb. 14, No. 5, 397-407 (1993).

Summary: We prove that there is a unique graph (on 56 vertices) with spectrum \(10^ 1 2^{35}(-4)^{20}\) and examine its structure. It turns out that, e.g., the Coxeter graph (on 28 vertices) and the Sylvester graph (on 36 vertices) are induced subgraphs. We give several descriptions of this graph.

MSC:

05C50	Graphs and linear algebra (matrices, eigenvalues, etc.)
05E30	Association schemes, strongly regular graphs

Keywords:

Gewirtz graph; graph spectra; spectrum; Coxeter graph; Sylvester graph