ON THE MATCHING POLYNOMIAL OF A POLYGRAPH

In this note we give an explanation for two phenomena mentioned in the concluding remarks of ''The matching polynomial of a polygraph'' by B abic et al. The following results are obtained: (1) Although three mat rices for given polygraphs defined in the above article in general hav e different orders, they determine the same recurrence relations for t he matching polynomial of these polygraphs. (2) Under certain symmetry conditions, the order of the recurrence relations can be reduced by a lmost a half.