"selecting in all possible ways an

unordered pair of X atoms and replacing the chosen X's by atoms of type Y."

Let us recall that an undirected graphG is a couple (V,E), where V is the set of vertices and E the set of edges, and an edge is an

unordered pair of vertices.

A graph G = (V, E) is a mathematical structure which consists of two sets V and E, where V is finite and nonempty, and every element of E is an

unordered pair {u, v} of distinct elements of V; we simply write uv instead of {u, v}.

Note that the body is an

unordered pair. The degree of a pair (u, v) is the number of vertices w that form an edge u, v [right arrow] w with the pair.

Clearly, the formal semantics would be more elaborate, since a finite sequence of blobs, rather than an ordered pair, is the interpretation of a directed edge, and a finite set thereof, rather than an

unordered pair, is the interpretation of an undirected edge.

* [phi] is an involution (because T' [omicron] [[tau].sub.T,T'] and T' have the same rows and, therefore, the

unordered pair {i, j} is the same for the two pairs of fillings);

Now we only have to show that an

unordered pair ([F.sub.1], [F.sub.2]) of spanning forests with two components each of which contains at least one vertex of {v, w, x} is counted with coefficient 1 on the right hand side of (2) if the union is a spanning tree and with coefficient 0 otherwise.

By "simple", we mean that there is at most one arc (directed edge) between any

unordered pair of vertices.

Graph G consists of a finite nonempty set V of p points (vertex) together with a prescribed set X of q

unordered pairs of distinct points of V.

A graph G is a pair (V (G), E (G)) of a set V (G) of vertices and a set E(G) of

unordered pairs of vertices, called edges.