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arXiv · 1704.02675

Largest regular multigraphs with three distinct eigenvalues

Hiroshi Nozaki
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Abstract

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 $k\ne 2,3,7,57$, we show an upper bound $n\leq k^2-k+1$, with equality if and only if there exists a finite projective plane of order $k-1$ that admits a polarity.

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Hiroshi Nozaki. 2019-04-10. Largest regular multigraphs with three distinct eigenvalues. https://arxiv.org/abs/1704.02675

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