Digraphs with Isomorphic Underlying and Domination Graphs: Connected UG^c(D)

Authors

Kim A. S. FactorFollow
Larry J. Langley, University of the Pacific

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.

Comments

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

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