  In [3] L.Zapponi studied the arithmetic of plane bipartite trees with prime
number of edges. He obtained a lower bound on the degree of tree's definition
field. Here we obtain a similar lower bound in the following case. There exists
a prime number $p$ such, that: a) the number of edges is divisible by $p$, but
not by $p^2$; b) for any proper subset of the set of white (or black) vertices
the sum of their degrees is not divisible by this $p$.

Number Theory