منابع مشابه
Signed total Italian k-domination in graphs
Let k ≥ 1 be an integer, and let G be a finite and simple graph with vertex set V (G). A signed total Italian k-dominating function (STIkDF) on a graph G is a functionf : V (G) → {−1, 1, 2} satisfying the conditions that $sum_{xin N(v)}f(x)ge k$ for each vertex v ∈ V (G), where N(v) is the neighborhood of $v$, and each vertex u with f(u)=-1 is adjacent to a vertex v with f(v)=2 or to two vertic...
متن کاملSecure Domination in Graphs
Let G=(V,E) be a graph. A subset S of V is a dominating set of G if every vertex in V \ S is adjacent to a vertex in S. A dominating set S is called a secure dominating set if for each v V \ S there exists u S such that v is adjacent to u and S1=(S-{u}) {v} is a dominating set. In this paper we introduce the concept of secure irredundant set and obtain an inequality chain of four parameters.
متن کاملSecure domination and secure total domination in graphs
A secure (total) dominating set of a graph G = (V, E) is a (total) dominating set X ⊆ V with the property that for each u ∈ V − X , there exists x ∈ X adjacent to u such that (X − {x}) ∪ {u} is (total) dominating. The smallest cardinality of a secure (total) dominating set is the secure (total) domination number γs(G) (γst(G)). We characterize graphs with equal total and secure total domination...
متن کاملSecure Edge Domination in Graphs
Let G = (V, E) be a graph without isolated vertices. A secure edge dominating set of G is an edge dominating set F⊆E with the property that for each e ∈ E – F, there exists f∈F adjacent to e such that (F – {f}) ∪ {e} is an edge dominating set. The secure edge domination number γ's(G) of G is the minimum cardinality of a secure edge dominating set of G. In this paper, we initiate a study of the ...
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...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Optimization
سال: 2020
ISSN: 1382-6905,1573-2886
DOI: 10.1007/s10878-020-00658-1