In the bottom figure Using AD to compute how many pathscycle

In the bottom figure: Using A(D) to compute how many paths/cycles from v1 to v4 with lengths 1, 2, 3, 4? how many paths/cycles with length 4?

Solution

1. A Cycle in a directed graph is a closed walk where all the vertices are different. Here vertices are V1,V2,V3 and V4.

Cycle from V1 to V4 -> Here if we see that a closed walk will be V1>V2>V3>V4>V3>V1 but, here V3 is repeated. Hence we can say that there is no cycle from V1 to V4,

2. There is no any cycle with Length 4.