The question becomes more general if [K.sub.n] is replaced by some (simple) graph G on n

vertices. If the answer is yes, we say that [pi] can be embedded into G, or equivalently, [pi] packs with [babr.G].

In this type of networks, intrinsic relationship structure of

vertices is a key factor to measure uniqueness of characters.

In any two-hole span coloring of a Type-II tree T with [DELTA] [greater than or equal to] 3, all major

vertices receive either the same color or the colors from any one of the sets {0,2}, {0, [DELTA] + 2}, or {[DELTA], [DELTA + 2}.

The other

vertices of the path are selected greedily by selecting the smallest degree neighbour among the unvisited neighbours.

Each group consists of two new

vertices, called son

vertices.

If G is a regular graph of degree r, with n

vertices and edges; then

The adaptive authentication algorithm feeds the number of neighboring

vertices, the watermark, and the x, y coordinates for the processing vertex into the hash function.

First, the set of monitored

vertices is monotone by inclusion, i.e.

Let [C.sub.6] be a cycle of length six and [GAMMA] be a graph obtained by connecting an isolated vertex to one of the

vertices of [C.sub.6].

Firstly, double color graph (DCG) is established as follows: represent the gears and planet carrier with solid

vertices "*," gear joints with hollow

vertices "[DELTA]," and revolute joint with hollow

vertices "**." And connect corresponding solid vertex and hollow vertex with an edge when a gear or a planet carrier is connected with a gear joint or a revolute joint.

The corona G1 G2 of the graphs G1 and G2 is defined as a graph obtained by taking one copy of G1 (with p

vertices) and p copies of G2 and then joining the ith vertex of G1 to every vertex of the ith copy of G2.

The cycle [C.sub.n] is a connected graph on n

vertices each with degree two.