In this note we give an explanation for two phenomena mentioned in the concluding remarks of “The matching polynomial of a polygraph” by Babic et al. The following results are obtained: #R##N#1.#R##N#Although three matrices for given polygraphs defined in the above article in general have different orders, they determine the same recurrence relations for the matching polynomial of these polygraghs.#R##N#2.#R##N#Under certain symmetry conditions, the order of the recurrence relations can be reduced by almost a half.
['Hajo Broersma', 'Li Xueliang']
On “the matching polynomial of a polygraph”