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NautyGraphs :: neighborhoodComplements

neighborhoodComplements -- complements the neighborhood for each vertex, individually

Synopsis

Description

The method creates a list of graphs, one for each vertex of the original graph G. The graph associated to a vertex v of G has the neighborhood of v complemented.

The method does not remove isomorphs.

i1 : neighborhoodComplements graph {{1,2},{1,3},{2,3},{3,4},{4,5}}

o1 = {Graph{0 => {1, 2}      }, Graph{0 => {1, 2, 3, 4}}, Graph{0 => {1, 2,
            1 => {0, 2, 3, 4}         1 => {0, 2}               1 => {0, 2,
            2 => {1, 0, 4}            2 => {1, 0, 4}            2 => {1, 0,
            3 => {1, 4}               3 => {0, 4}               3 => {2}   
            4 => {1, 2, 3}            4 => {0, 2, 3}            4 => {1, 0}
     ------------------------------------------------------------------------
     4}}, Graph{0 => {1, 4}   }, Graph{0 => {1, 2, 3}}}
     4}         1 => {0, 4}            1 => {0, 2, 3}
     3}         2 => {3}               2 => {1, 0}
                3 => {2, 4}            3 => {1, 0, 4}
                4 => {1, 0, 3}         4 => {3}

o1 : List

See also

Ways to use neighborhoodComplements :