Abstract
The parameter q(G) of a graph G is the minimum number of distinct eigenvalues over the family of symmetric matrices described by G. It is shown that the minimum number of edges necessary for a connected graph G to have q(G)=2 is 2n−4 if n is even, and 2n−3 if n is odd. In addition, a characterization of graphs for which equality is achieved in either case is given.
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