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An Explicit Construction of Optimal Dominating Sets in Grid
A dominating set in a graph is a subset of vertices such that every
vertex in is a neighbor of some vertex of . The domination
number of is the minimum size of a dominating set of and it is denoted
by . Also, a subset of a graph is a -set if,
each vertex is adjacent to either one or two vertices in
and the minimum cardinality of -dominating set of , is
denoted by . Chang's conjecture says that for every ,
and this conjecture has been proven by Goncalves et al. This paper presents an
explicit constructing method to find an optimal dominating set for grid graph
where in . In addition, we
will show that where
holds in response to an open question posed by Chellali et al