BUILT-IN MATHEMATICA SYMBOL

IndependentEdgeSetQ

yields True if the edge list elist is an independent edge set of the graph g, and False otherwise.

An independent edge set is a set of edges that are never incident to the same vertex.

Test whether a set of edges is an independent edge set:

Test for a directed graph:

Test whether a set of edges is an independent edge set:

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Test for a directed graph:

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Test undirected graphs:

Enumerate all independent edge sets for a cycle graph:

Enumerate all subsets of edges and select the independent edge sets:

Highlight independent sets:

Enumerate all maximal independent edge sets for a wheel graph:

Find the length of a maximal independent edge set:

Enumerate all edge subsets of length 2 and select the independent edge sets:

Highlight maximal independent sets:

A largest independent edge set can be found using FindIndependentEdgeSet:

Bipartite graphs have independent edge sets and vertex covers of equal length:

For a graph without isolated vertices, the sum of the size of the independent edge set and the size of the edge cover equals the number of vertices: