For a given undirected graph
G, let V(G) be the set of its vertices and let E(G) be the set of its edges.
The communication topology of the WSN can be modeled by a time-varying undirected graph
, G([t.sup.i.sub.s]), where i = 1, ..., n and s [member of] N.
A network is represented as an undirected graph
G = (N, L) consisting of N = [absolute value of N] nodes and L = [absolute value of L] links.
Unfortunately, the problem of determining the MCDS in an undirected graph
, like that of the unit disk graph considered for modeling MANETs, is NP-complete.
Let us consider a simple (without loops and multiple edges) undirected graph
For any finite, simple, undirected graph
[GAMMA] = [GAMMA](V,E), the adjacency matrix A = ([a.sub.ij]) is defined as follows:
It is a directed or undirected graph
consisting of vertexes, which represent concepts, and edges.
The key to the solution of our problem is the rotation graph, an undirected graph
of m nodes with a connection between node i and node j if a rotation is allowed in plane (i, j).
Any undirected graph
with minimum cut c contains a tree packing of value at least c/2.
On the other hand, a (finite) undirected graph
G = (V, E, *) contains only one function *:E *[W * V 1 [is less than or= W [is less than or =] 2], assigning up to two vertices to every edge.
In an undirected graph
, we assume that there are k nodes.
We can model this problem as a graph-theoretical one: First, an undirected graph
G = (V, E) where V is the set of peptides P, and the edge set E contains an edge [p.sub.i][p.sub.j] (or a loop at [p.sub.i], denoted by [p.sub.i][p.sub.i]) if and only if [p.sub.i] and [p.sub.j] interact.