A spectral characterization of strongly distance-regular graphs with diameter four

2014/07/05 by M.A. Fiol, M. A. Fiol, Fiol, M. A.
Mathematics · Neuroscience · #Finite Group Theory Research #Graph theory and applications #Nuclear Receptors and Signaling #math.CO #msc:05C50 #msc:05E30

paper · pdf · doi:10.48550/arxiv.1407.1392

arxiv created 2014/07/05 · arxiv updated 2014/07/08

Abstract

A graph G with d+1 distinct eigenvalues is called strongly distance-regular if G itself is distance-regular, and its distance-d graph G_d is strongly-regular. In this note we provide a spectral characterization of those distance-regular graphs with diameter d=4 which are strongly distance-regular. As a byproduct, it is shown that all bipartite strongly distance-regular graphs with such a diameter are antipodal.

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