This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
 BUILT-IN MATHEMATICA SYMBOL

# EdgeCoverQ

 EdgeCoverQ yields True if the edge list elist is an edge cover of the graph g and False otherwise.
• An edge cover is a set of edges that is incident to every vertex.
Test whether a set of edges is an edge cover of a complete graph:
Test for a directed graph:
Test whether a set of edges is an edge cover of a complete graph:
 Out[1]=
 Out[2]=

Test for a directed graph:
 Out[1]=
 Out[2]=
 Scope   (2)
Test undirected graphs:
Directed graphs:
 Applications   (2)
Enumerate all edge covers:
Enumerate all subsets of edges and select the covers:
Highlight covers:
Enumerate all minimal edge covers:
Find the length of a minimal edge cover:
Enumerate all edge subsets of length 3 and select the covers:
Highlight minimal covers:
For a graph without isolated vertices, the EdgeList is an edge cover:
A smallest edge cover can be found using FindEdgeCover:
The complete bipartite graph has edge cover of size :
For a connected graph, the total size of an independent edge set and an edge cover equals the number of vertices:
New in 8