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Characterization Of Digraphs With Equal Domination Graphs And Underlying Graphs, Kim A. S. Factor, Larry J. Langley
Characterization Of Digraphs With Equal Domination Graphs And Underlying Graphs, Kim A. S. Factor, Larry J. Langley
Mathematics, Statistics and Computer Science Faculty Research and Publications
A domination graph of a digraph D , dom(D)dom(D), is created using the vertex set of D and edge {u,v}∈E[dom(D)]{u,v}∈E[dom(D)] whenever (u,z)∈A(D)(u,z)∈A(D) or (v,z)∈A(D)(v,z)∈A(D) for every other vertex z∈V(D)z∈V(D). The underlying graph of a digraph DD, UG(D)UG(D), is the graph for which D is a biorientation. We completely characterize digraphs whose underlying graphs are identical to their domination graphs, UG(D)=dom(D)UG(D)=dom(D). The maximum and minimum number of single arcs in these digraphs, and their characteristics, is given.