# Digraphs with Isomorphic Underlying and Domination Graphs: Connected *UG*^{c}(D)

^{c}(D)

## Document Type

Article

## Language

eng

## Format of Original

17 p.

## Publication Date

2007

## Publisher

Elsevier

## Source Publication

Discrete Mathematics

## Source ISSN

1872-681X

## 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, Kim A. S. and Langley, Larry J., "Digraphs with Isomorphic Underlying and Domination Graphs: Connected *UG ^{c}(D)*" (2007).

*Mathematics, Statistics and Computer Science Faculty Research and Publications*. 452.

https://epublications.marquette.edu/mscs_fac/452

## Comments

Discrete Mathematics, Vol. 27, No. 1 (2007): 51-67. DOI.