Dominating sets play an important role in applications of graph theory. Recent studies in this field studied properties of minimum dominating sets (γ-set). The other type of studies produces a topology space from the set of vertices or the set of edges of a graph G. In this paper, the domination topology (τd) has been created form the set of minimal dominating sets of a graph G. The family of all minimal dominating sets (MDS) represents open sets in τd. The (∧d) d-intersection and (∨d) d-union have been defined.
Topics
Graph theory
REFERENCES
1.
C.
Berge
, The Theory of Graphs and its Applications, Methuen and Co
, London
, 1962
.2.
J.L.
Gross
, J.
Yellen
and P.
Zhang
, Handbook of Graph Theory (Second edition), CRC press
, 2014
.3.
K.P.
Hart
et al., Encyclopedia of General Topology, Elsevier
, North-Holland
, 2004
.4.
T.W.
Haynes
, S.T.
Hedetniemi
and P.J.
Slater
, Fundamentals of Domination in Graphs, Marcel Dekker, Inc
., New York
, 1998
.5.
A.A.
Jabor
and A.A.
Omran
, Domination in discrete topology graph
, AIP Conf. Proc.
2183
, 030006
(2019
).6.
S.
Nada
, A.
El Atik
and M. Atef1, New types of topological structures via graphs, Wiley
: Special issue, 1
–10
(2017
) doi: .7.
A.A.
Omran
and H.H.
Oda
, Hn-domination in graphs
, Baghdad Sci. J.
16
:1
, 242
–247
(2019
).8.
A.A.
Omran
and R.
Yasen
, Some properties of frame domination in graphs
, JEAS
12
:10
, 882
–885
(2017
).9.
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