Shunyi Liu, Jinjun Ren
Published 2014-11-01Version 1
Merris et al. formulated that the permanental polynomial seems a little better than the characteristic polynomial when it comes to distinguishing graphs which are not trees, since they found that there exist five pairs of cospectral graphs which can be distinguished by the permanental polynomial [R. Merris, K.R. Rebman and W. Watkins, Permanental polynomials of graphs, Linear Algebra Appl. 38 (1981) 273--288]. It is natural to ask whether the permanental polynomial really in general performs better than characteristic polynomial when we use them to distinguish graphs. In this paper, we determine the permanental polynomials for all graphs on at most 11 vertices, and count the numbers for which there is at least one other graph with the same permanental polynomial. A comparision of the present data between permanental and characteristic polynomials shows that Merris et al.'s formulation is true.
Comments: 14 pages, 1 figure
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