On the number of simple eigenvalues of a graph

Citation

Rowlinson P (1983) On the number of simple eigenvalues of a graph. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 94 (3-4), pp. 247-250. https://doi.org/10.1017/S0308210500015626

Abstract
Let Γ be a graph with n points, and let G be the group of automorphisms of Γ. An orbit of G on which G acts as an elementary abelian 2-group is said to be exceptional. It is shown that the number of simple eigenvalues of Γ is at most (5n+4t)/9, where t is the number of points of Γ lying in exceptional orbits of G.

Journal
Proceedings of the Royal Society of Edinburgh: Section A Mathematics: Volume 94, Issue 3-4