@MISC{Dousse11stronglyconnected, author = {Jehanne Dousse}, title = {Strongly connected graphs and polynomials}, year = {2011} }

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Abstract

In this report, we give the exact solutions ofthe equation P(A) = 0 where P is a polynomial of degree2 with integer coefficients, and A is the adjacency matrix of a strongly connected graph. Then we study the problem for P a polynomial of degree n ≥ 3, and give a necessary condition on the trace of a rank one matrix. Finally, we give the solutions of maximal size in some particular cases. 1