A New Approach to the Spectral Excess Theorem for Distance-Regular Graphs
نویسندگان
چکیده
The Spectral Excess Theorem provides a quasi-spectral characterization for a (regular) graph Γ with d+1 different eigenvalues to be distance-regular graph, in terms of the mean (d-1)-excess of its vertices. The original approach, due to Fiol and Garriga in 1997, was obtained in a wide context from a local point of view, so giving a characterization of the so-called pseudo-distanceregularity around a vertex. In this paper we present a new simple method based in a global point of view, and where the mean degree of the distance-d graph Γd plays an essential role.
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تاریخ انتشار 2009