GATE Computer Science (CS) 2022 Shift 1 Solved Paper

Let G (V, E) be a directed graph, where V = {1, 2, 3, 4, 5} is the set of vertices and E is the set of directed edges, as defined by the following adjacency matrix A.

A[𝑖][𝑗] = 1 indicates a directed edge from node i to node j. A directed spanning tree of G, rooted at r ∈ V, is defined as a subgraph T of G such that the undirected version of T is a tree, and T contains a directed path from r to every other vertex in V. The number of such directed spanning trees rooted at vertex 5 is ______