For each vertex v in a graph G, let there be associated a subgraph H_v of G. The vertex v is said to dominate H_v as well as dominate each vertex and edge of H_v. A set S of vertices of G is called a full dominating set if every vertex of G is dominated by some vertex of S, as is every edge of G. The minimum cardinality of a full dominating set of G is its full domination number γ_FH(G). A full dominating set of G of cardinality γ_FH(G) is called a γ_FH-set of G. We study three types of full domination in graphs: full star domination, where H_v is the maximum star centered at v, full closed domination, where H_v is the subgraph induced by the closed neighborhood of v, and full open domination, where H_v is the subgraph induced by the open neighborhood of v.
@article{DMGT_2001_21_1_a3,
author = {Brigham, Robert and Chartrand, Gary and Dutton, Ronald and Zhang, Ping},
title = {Full domination in graphs},
journal = {Discussiones Mathematicae. Graph Theory},
pages = {43--62},
year = {2001},
volume = {21},
number = {1},
language = {en},
url = {http://geodesic.mathdoc.fr/item/DMGT_2001_21_1_a3/}
}
TY - JOUR
AU - Brigham, Robert
AU - Chartrand, Gary
AU - Dutton, Ronald
AU - Zhang, Ping
TI - Full domination in graphs
JO - Discussiones Mathematicae. Graph Theory
PY - 2001
SP - 43
EP - 62
VL - 21
IS - 1
UR - http://geodesic.mathdoc.fr/item/DMGT_2001_21_1_a3/
LA - en
ID - DMGT_2001_21_1_a3
ER -
%0 Journal Article
%A Brigham, Robert
%A Chartrand, Gary
%A Dutton, Ronald
%A Zhang, Ping
%T Full domination in graphs
%J Discussiones Mathematicae. Graph Theory
%D 2001
%P 43-62
%V 21
%N 1
%U http://geodesic.mathdoc.fr/item/DMGT_2001_21_1_a3/
%G en
%F DMGT_2001_21_1_a3
