Results 11 to 20 of about 897 (158)
On Domatic Number of Some Rotationally Symmetric Graphs [PDF]
Journal of Mathematics, 2023 Domination is a well-known graph theoretic concept due to its significant real-world applications in several domains, such as design and communication network analysis, coding theory, and optimization.
Hassan Raza +2 more
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The Italian domatic number of a digraph [PDF]
Communications in Combinatorics and Optimization, 2019 An {\em Italian dominating function} on a digraph $D$ with vertex set $V(D)$ is defined as a function $f\colon V(D)\to \{0, 1, 2\}$ such that every vertex $v\in V(D)$ with $f(v)=0$ has at least two in-neighbors assigned 1 under $f$ or one in-neighbor ...
L.Volkmann
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Strong domatic number of a graph [PDF]
Discrete Mathematics, Algorithms and Applications, 2023 A set [Formula: see text] of vertices of a simple graph [Formula: see text] is a strong dominating set, if for every vertex [Formula: see text] there is a vertex [Formula: see text] with [Formula: see text] and [Formula: see text]. The strong domination number [Formula: see text] is defined as the minimum cardinality of a strong dominating set.
Nima Ghanbari, Saeid Alikhani
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Vertex-Domatic, Edge-Domatic and Total Domatic Number of Uniform Hypergraphs [PDF]
, 2020 Submitted to "Information Processing Letters, Elsevier"
Smruti Dash
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On the b-Domatic Number of Graphs
Discussiones Mathematicae Graph Theory, 2019 A set of vertices S in a graph G = (V, E) is a dominating set if every vertex not in S is adjacent to at least one vertex in S. A domatic partition of graph G is a partition of its vertex-set V into dominating sets. A domatic partition 𝒫 of G is called b-
Benatallah Mohammed +2 more
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Upper Bounds on the Signed Total (K, K)-Domatic Number of Graphs
Discussiones Mathematicae Graph Theory, 2015 Let G be a graph with vertex set V (G), and let f : V (G) → {−1, 1} be a two-valued function. If k ≥ 1 is an integer and Σx∈N(v) f(x) ≥ k for each v ∈ V (G), where N(v) is the neighborhood of v, then f is a signed total k-dominating function on G. A set {
Volkmann Lutz
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Edge-domatic number of a graph [PDF]
Czechoslovak Mathematical Journal, 1983 An edge-dominating set of a graph G is a subset D of the edge set E(G) with the property that for each edge \(e\in E(G)-D\) there exists at least one edge \(f\in D\) adjacent to e. The maximum number of classes of partitions of E(G) into edge-dominating sets is called the edge-domatic number of G and is denoted by ed(G).
Bohdan Zelinka
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The Numerical Invariants concerning the Total Domination for Generalized Petersen Graphs
Journal of Mathematics, 2020 A subset S of VG is called a total dominating set of a graph G if every vertex in VG is adjacent to a vertex in S. The total domination number of a graph G denoted by γtG is the minimum cardinality of a total dominating set in G.
Taiyin Zhao +4 more
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The Signed Total Roman k-Domatic Number Of A Graph
Discussiones Mathematicae Graph Theory, 2017 Let k ≥ 1 be an integer. A signed total Roman k-dominating function on a graph G is a function f : V (G) → {−1, 1, 2} such that Ʃu2N(v) f(u) ≥ k for every v ∈ V (G), where N(v) is the neighborhood of v, and every vertex u ∈ V (G) for which f(u) = −1 is ...
Volkmann Lutz
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On the total domatic number of regular graphs [PDF]
Transactions on Combinatorics, 2012 A set S of vertices of a graph G = (V;E) without isolated vertex is a total dominating set if every vertex of V (G) is adjacent to some vertex in S.
H. Aram +2 more
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