Counting the number of minimum cuts in undirected multigraphs

Abstract

The problem of counting the number of cuts with the minimum cardinality in an undirected multigraph arises in various applications, such as testing the super- lambda -ness of a graph, as described by F.T. Boesch (1986), and calculating upper and lower bounds on the probabilistic connectedness of a stochastic graph G in which edges are subject to failure. It is shown that the number mod C(G) mod of cuts with the minimum cardinality lambda (G) in a multiple graph G=(V,E) can be computed in O( mod E mod + lambda (G) mod V mod /sup 2/+ lambda (G) mod C(G) mod mod V mod ) time. >