An Algorithm for Enumerating All Spanning Trees of a Directed Graph

We present an O(NV +V 3) time algorithm for enumerating all spanning trees of a directed graph. This improves the previous best known bound of O(NE + V + E) [1] when V 2 = o(N), which will be true for most graphs. Here, N refers to the number of spanning trees of a graph having V vertices and E edges. The algorithm is based on the technique of obtaining one spanning tree from another by a series of edge swaps. This result complements the result in the companion paper [3] which enumerates all spanning trees in an undirected graph in O(N + V + E) time. Key Words. Spanning tree, Directed graph, Enumeration.

• Type: Journal
• Year: 2000
• Where: ALGORITHMICA
• Authors: Sanjiv Kapoor, H. Ramesh
• Keywords: ALGORITHMICA 2000, Directed Graph, NV +V, Time Algorithm