@article{oai:aue.repo.nii.ac.jp:00007371, author = {Nozaki, Hiroshi}, issue = {7}, journal = {Discrete Mathematics}, month = {Jul}, note = {text, We deal with connected k-regular multigraphs of order n that has only three distinct eigenvalues. In this paper, we study the largest possible number of vertices of such a graph for given k. For k = 2; 3; 7, the Moore graphs are largest. For k ≠ 2; 3; 7; 57, we show an upper bound n ≤ k2 - k + 1, with equality if and only if there exists a nite projective plane of order k - 1 that admits a polarity.}, pages = {2134--2138}, title = {Largest regular multigraphs with three distinct eigenvalues}, volume = {342}, year = {2019} }