Question

I am working on an assignment where one of the problems asks to derive an algorithm to check if a directed graph G=(V,E) is singly connected (there is at most one simple path from u to v for all distinct vertices u,v of V.

Of course you can brute force check it, which is what I’m doing right now, but I want to know if there’s a more efficient way. Could anyone point me in the right direction?

Answer 1

Have you tried DFS.

Run DFS for every vertex in the graph as source
    If a visited vertex is encountered again, the graph is not singly connected
repeat for every unvisited vertex.
The graph is singly connected.

Complexity O(v^2), o(v) dfs as no repetition.