Abstract
Two algorithms for the evaluation of the characteristic polynomial of a graph G are described. Both algorithms have the operation count of the order n 3, where n is the number of the vertices in the graph G. These algorithms are stable, fast, and efficient. They are one order of magnitude faster than the Le Verrier-Faddeev-Frame method, which is presently claimed to be the most efficient method for the calculation of the characteristic polynomial of a graph. A related problem of finding a characteristic polynomial from the known eigenvalues λ i of the adjacency matrix is also considered. An algorithm requiring only O( n 2) operations is described.
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