3 docs tagged with "successor-graphs"

Consider a successor graph that only contains a path that ends in a cycle. We may ask the following questions: if we begin our walk at the starting node, what is the first node in the cycle and how many nodes does the cycle contain? For example, in Fig. 34, we begin our walk at node 1, the first node that belongs to the cycle is node 4, and the cycle consists of three nodes (4, 5, and 6).

Since each node of a successor graph has a unique successor, we can also define a function succ(x, k) that gives the node that we will reach if we begin at node x and walk k steps forward. For example, in our example graph succ(4, 6) = 2, because we will reach node 2 by walking 6 steps from node 4 (Fig. 33).

Successor Graphs