The Spectral Excess Theorem for Distance-Biregular Graphs.

Miquel Àngel Fiol


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.


Distance-biregular graph; Spectral excess theorem; Orthogonal polynomials

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