# Digraphs with isomorphic underlying and domination graphs: connected $U{G}^{c}\left(d\right)$

Kim A.S. Factor; Larry J. Langley

Discussiones Mathematicae Graph Theory (2007)

- Volume: 27, Issue: 1, page 51-67
- ISSN: 2083-5892

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topKim A.S. Factor, and Larry J. Langley. "Digraphs with isomorphic underlying and domination graphs: connected $UG^c(d)$." Discussiones Mathematicae Graph Theory 27.1 (2007): 51-67. <http://eudml.org/doc/270289>.

@article{KimA2007,

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.},

author = {Kim A.S. Factor, Larry J. Langley},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {domination graph; domination; graph isomorphism; underlying graph; characterization},

language = {eng},

number = {1},

pages = {51-67},

title = {Digraphs with isomorphic underlying and domination graphs: connected $UG^c(d)$},

url = {http://eudml.org/doc/270289},

volume = {27},

year = {2007},

}

TY - JOUR

AU - Kim A.S. Factor

AU - Larry J. Langley

TI - Digraphs with isomorphic underlying and domination graphs: connected $UG^c(d)$

JO - Discussiones Mathematicae Graph Theory

PY - 2007

VL - 27

IS - 1

SP - 51

EP - 67

AB - 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.

LA - eng

KW - domination graph; domination; graph isomorphism; underlying graph; characterization

UR - http://eudml.org/doc/270289

ER -

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