The Spectral Excess Theorem for Distance-Biregular Graphs.

  • Miquel Àngel Fiol
Keywords: Distance-biregular graph, Spectral excess theorem, Orthogonal polynomials


The spectral excess theorem for distance-regular graphs states that a regular (connected) graph is distance-regular if and only if its spectral-excess equals its average excess. A bipartite graph $\Gamma$ is distance-biregular when it is distance-regular around each vertex and the intersection array only depends on the stable set such a vertex belongs to. In this note we derive a new version of the spectral excess theorem for bipartite distance-biregular graphs.
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