منابع مشابه
The 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.
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The open neighborhood of a vertex $v$ of a graph $G$ is the set $N(v)$ consisting of all vertices adjacent to $v$ in $G$. For $Dsubseteq V(G)$, we define $overline{D}=V(G)setminus D$. A set $Dsubseteq V(G)$ is called a super dominating set of $G$ if for every vertex $uin overline{D}$, there exists $vin D$ such that $N(v)cap overline{D}={u}$. The super domination number of $G$ is the minimum car...
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A graph G is 2-stratified if its vertex set is colored into two nonempty classes, where one class of vertices colored red and the other color class blue. Let F be a 2-stratified graph rooted at one fixed blue vertex v. The F -domination number of G is the minimum number of red vertices of G in a red-blue coloring of the vertices of G such that for every blue vertex v of G, there is a copy of F ...
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In this paper, we investigate domination number as well as signed domination numbers of Cay(G : S) for all cyclic group G of order n, where n in {p^m; pq} and S = { a^i : i in B(1; n)}. We also introduce some families of connected regular graphs gamma such that gamma_S(Gamma) in {2,3,4,5 }.
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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 ...
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2011
ISSN: 0895-4801,1095-7146
DOI: 10.1137/11082574