-partition boards and poly-Stirling numbers.
The mean value of the matching polynomial is computed in the family of all labeled graphs with n vertices. We introduce the dominating polynomial of a graph whose coefficients enumerate the dominating sets for a graph and study some properties of the polynomial. The mean value of this polynomial is determined in a certain special family of bipartite digraphs.
We prove that, for any prime , there are precisely medial quasigroups of order , up to isomorphism.