Abstract
A semiregular graph is a bipartite graph which, from the point of view of the vertices of one of the partite sets, appears to be regular. Many facts about distance-regular graphs remain true for this class: the adjacency matrix has d + 1 eigenvalues (d=diameter); the eigenmatnx associated with the second eigenvalue can provide a representation of the automorphism group; the coloration matrix represents the adjacency matrix in the span of the distance matrices, and its eigenvectors provide eigenvectors of the adjacency matrix.
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