A minimum edge cover is an edge cover having the smallest possible number of edges for a given graph. The size of a minimum edge cover of a graph is known as the edge cover number of G and is denoted ρ(G). Every minimum edge cover is a minimal edge cover (i.e., not a proper subset of any other edge cover), but not necessarily vice versa. Only graphs with no isolated points have an edge cover (and therefore a minimum edge cover). A minimum edge cover of a graph can be computed in the Wolfram Language with FindEdgeCover[g]. There is currently no Wolfram Language function to compute all minimum edge covers of a graph.

edge cover | minimal edge cover