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