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{\bf Edwin R. van Dam}
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{\bf The Spectral Excess Theorem for Distance-Regular Graphs: A Global (Over)view}
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Distance-regularity of a graph is in general not determined by the
spectrum of the graph. The spectral excess theorem states that a
connected regular graph is distance-regular if for every vertex, the
number of vertices at extremal distance (the excess) equals some given
expression in terms of the spectrum of the graph. This result was
proved by Fiol and Garriga [From local adjacency polynomials to
locally pseudo-distance-regular graphs, {\it J. Combinatorial Th. B}
71 (1997), 162-183] using a local approach. This approach has the
advantage that more general results can be proven, but the
disadvantage that it is quite technical. The aim of the current paper
is to give a less technical proof by taking a global approach.



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