منابع مشابه
Independent [1, 2]-domination of grids via min-plus algebra
Domination of grids has been proved to be a demanding task and with the addition of independence it becomes more challenging. It is known that no grid withm,n ≥ 5 has a perfect code, that is an independent vertex set such that each vertex not in it has exactly one neighbor in that set. So it is interesting to study the existence of an independent dominating set for grids that allows at most two...
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A Roman dominating function (RDF) on a graph G=(V,E) is a function f : V → {0, 1, 2} such that every vertex u for which f(u)=0 is adjacent to at least one vertex v for which f(v)=2. An RDF f is calledan outer independent Roman dominating function (OIRDF) if the set ofvertices assigned a 0 under f is an independent set. The weight of anOIRDF is the sum of its function values over ...
متن کاملIndependent domination in directed graphs
In this paper we initialize the study of independent domination in directed graphs. We show that an independent dominating set of an orientation of a graph is also an independent dominating set of the underlying graph, but that the converse is not true in general. We then prove existence and uniqueness theorems for several classes of digraphs including orientations of complete graphs, paths, tr...
متن کاملThe Domination Number of Grids
In this paper, we conclude the calculation of the domination number of all n×m grid graphs. Indeed, we prove Chang’s conjecture saying that for every 16 ≤ n ≤ m, γ(Gn,m) = ⌊ (n+2)(m+2) 5 ⌋ −4.
متن کاملPerfect Domination of Rectangular Grids
Let m and n be positive integers. The algorithmic search for perfect dominating sets of the rectangular grid Gm;n satisfying an initial condition S 0 de ned as an admissible subset of a side Gm;1 of Gm;n such that S \ Gm;1 = S 0 is considered. A binary decision algorithm that generates all such perfect dominating sets is presented, and some related questions and conjectures are posed, leading t...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2015
ISSN: 0012-365X
DOI: 10.1016/j.disc.2015.02.015