Page 108 - Intelligent Communication Systems

90 INTELLIGENT COMMUNICATION SYSTEMS

FIGURE 9.5 Graph vs. directed graph.

FIGURE 9.6 Cycle example.

branch, node / is the parent node of node j and nodey is the child node
of node i.
(3) Regardless of the direction of a branch, the sequence of the branches
bl,b2,...,bn that are connected together is called the walk of length n
and is defined as (bl, b2,..., bn).
When there is a sequence of nodes (b 1, b2,..., bn) linked by directed branches
and the ending point of hi is the beginning point of b(i +1), then the sequence is
called a path of length n. When there is a path (bl, b2,..., bn) and bl and bn are
the same, the path is called a cycle (Figure 9.6). If there is a walk for every node
in a graph, the graph is connected. The connected graph that has no cycle is called
a tree (Figure 9.7). The tree that has only one root is called & principal tree. If there
are two paths pi and/?2, where the first node of path/? 1 and that of pathp2 are the
same, the last node of path pi and that of path p2 are the same, and any other nodes
except the first node and the last node are different, then the paths are called a
circuit (Figure 9.8). A graph is shown in Figure 9.9.
The procedure for detecting the goal node by starting from the initial node is called
problem solving by using a state space. Let's study an example of problem solving.