Format of Original
Charles Babbage Research Center
Journal of Combinatorial Mathematics and Combinatorial Computing
A domination graph of a digraph D, dom (D), is created using thc vertex set of D and edge uv ϵ E (dom (D)) whenever (u, z) ϵ A (D) or (v, z) ϵ A (D) for any other vertex z ϵ A (D). Here, we consider directed graphs whose underlying graphs are isomorphic to their domination graphs. Specifically, digraphs are completely characterized where UGc (D) is the union of two disjoint paths.
Factor, Kim A. S. and Langley, Larry J., "Digraphs with Isomorphic Underlying and Domination Graphs: Pairs of Paths" (2010). Mathematics, Statistics and Computer Science Faculty Research and Publications. 15.