Title

Digraphs with isomorphic underlying and domination graphs: Connected UGc(D)

Authors

Kim A. S. Factor, Marquette UniversityFollow
Larry L. Langley, University of the PacificFollow

Document Type

Article

Publication Title

Discussiones Mathematicae Graph Theory

Department

Mathematics

ISSN

2083-5892

Volume

27

Issue

1

DOI

10.7151/dmgt.1344

First Page

51

Last Page

68

Publication Date

1-1-2007

Abstract

The domination graph of a directed graph has an edge between vertices x and y provided either (x,z) or (y,z) is an arc for every vertex z distinct from x and y. We consider directed graphs D for which the domination graph of D is isomorphic to the underlying graph of D. We demonstrate that the complement of the underlying graph must have k connected components isomorphic to complete graphs, paths, or cycles. A complete characterization of directed graphs where k = 1 is presented.

Recommended Citation

Factor, K. A., & Langley, L. L. (2007). Digraphs with isomorphic underlying and domination graphs: Connected UGc(D). Discussiones Mathematicae Graph Theory, 27(1), 51–68. DOI: 10.7151/dmgt.1344
https://scholarlycommons.pacific.edu/cop-facarticles/644