A digraph G = (i, E) contains a set i of vertices and a set E of arcs (i, j) leading from initial vertex i to
terminal vertex j.
A digraph G = (U, E) contains a set U = {1,2, ..., n} of vertices and a set E of arcs (i, j) leading from initial vertex i to
terminal vertex j.
If de[g.sub.G](v) = 1 then v is called a pendant vertex or a
terminal vertex. The distance between the vertices [v.sub.i] and [v.sub.j] in G is equal to the length of a shortest path joining them and is denoted by d([v.sub.i], [v.sub.j]|G).
The end vertex of the primary path is called the terminal vertex. Note that, the terminal vertex need not be an active vertex.
Let P be the primary path of V LR(i), [2.sup.d-1] < i < [2.sup.d] - 1, and [v.sub.tip], [v.sub.t] be the tip and the terminal vertex of P, respectively.
Finally consider the definition of a
terminal vertex as one with exactly one edge attached to it.
The algorithm described does not actually list the shortest path from the starting vertex to the terminal vertex; it only gives the shortest distance.
Step 2: Assign a permanent label [L.sub.n] = [E.sub.n] to the terminal vertex [v.sub.n] = n, and temporary label [E.sub.n] to the remaining n - 1 vertices.
We distinguish between three sorts of vertices by saying that v [member of] [V.sub.T] is: (a) a terminal vertex if it is the bottom or top vertex of some black tile; (b) an ordinary vertex if all tiles in [F.sub.T](v) are white; and (c) a mixed vertex otherwise (i.e.
Corollary 2.1 Let v be a terminal vertex belonging to a black ij-tile [tau].
Also, the total delay will not exceed a certain amount for any available route between the root and terminal vertexes.
In the mentioned problem, the high risk areas and the areas which involve the servers are considered as the root, and the other areas are considered as terminal vertexes. By solving the optimal problem which has been presented in Equation 10, the RSU installation places are determined and it will be guaranteed that the amount of delay in sending the traffic information between the selected areas and the other areas will not exceed certain bounds.