Edge Weighting Functions on Semitotal Dominating Sets
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DOI: 10.1007/s00373-017-1769-4
Abstract: A set S of vertices in an isolate-free graph G is a semitotal dominating set of G if it is a dominating set of G and every vertex in S is within distance 2 of another… read more here.
Keywords: domination number; semitotal dominating; edge weighting; dominating set ... See more keywords
On the Game Total Domination Number
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DOI: 10.1007/s00373-018-1883-y
Abstract: The total domination game is a two-person competitive optimization game, where the players, Dominator and Staller, alternately select vertices of an isolate-free graph G. Each vertex chosen must strictly increase the number of vertices totally… read more here.
Keywords: game; domination number; game total; total domination ... See more keywords
The Finite Projective Plane and the 5-Uniform Linear Intersecting Hypergraphs with Domination Number Four
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DOI: 10.1007/s00373-018-1921-9
Abstract: The matching number $$\alpha '(H)$$α′(H) of a hypergraph H is the size of a largest matching in H, where a matching is a set of pairwise disjoint edges in H. A dominating set in H… read more here.
Keywords: domination number; finite projective; intersecting hypergraphs; uniform linear ... See more keywords
The spectral radius and domination number in linear uniform hypergraphs
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DOI: 10.1007/s10878-019-00424-y
Abstract: This paper investigates the spectral radius and signless Laplacian spectral radius of linear uniform hypergraphs. A dominating set in a hypergraph H is a subset D of vertices if for every vertex v not in… read more here.
Keywords: uniform hypergraphs; linear uniform; domination number; radius ... See more keywords
Total k-domination in Cartesian product graphs
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DOI: 10.1007/s10998-017-0191-2
Abstract: Let $$G=(V,E)$$G=(V,E) be a graph. A set $$S\subseteq V$$S⊆V is a total k-dominating set if every vertex $$v\in V$$v∈V has at least k neighbors in S. The total k-domination number $$\gamma _{kt}(G)$$γkt(G) is the minimum… read more here.
Keywords: domination; total domination; domination number; cartesian product ... See more keywords
Influence of the Edge Removal, Edge Addition and Edge Subdivision on the Double Vertex–Edge Domination Number of a Graph
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DOI: 10.1007/s40009-018-0689-z
Abstract: A vertex v of a graph $$G=(V,E)$$G=(V,E) is said to ve-dominate every edge incident to v, as well as every edge adjacent to these incident edges. A set $$S \subseteq V$$S⊆V is a vertex–edge dominating… read more here.
Keywords: edge domination; domination number; double vertex; edge ... See more keywords
Double Roman Domination in Digraphs
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DOI: 10.1007/s40840-017-0582-9
Abstract: Let D be a finite and simple digraph with vertex set V(D). A double Roman dominating function (DRDF) on a digraph D is a function $$f:V(D)\rightarrow \{0,1,2,3\}$$f:V(D)→{0,1,2,3} satisfying the condition that if $$f(v)=0$$f(v)=0, then the… read more here.
Keywords: domination number; double roman; roman domination; domination ... See more keywords
A General Lower Bound for the Domination Number of Cylindrical Graphs
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DOI: 10.1007/s40840-019-00765-1
Abstract: In this paper, we present a lower bound for the domination number of the Cartesian product of a path and a cycle that is tight if the length of the cycle is a multiple of… read more here.
Keywords: bound; domination number; lower bound; bound domination ... See more keywords
[1, k]-Domination Number of Lexicographic Products of Graphs
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DOI: 10.1007/s40840-020-00957-0
Abstract: A subset D of the vertex set V ( G ) of a graph G is called a [1, k ]-dominating set if every vertex from $$V-D$$ V - D is adjacent to at least… read more here.
Keywords: domination number; number lexicographic; number; products graphs ... See more keywords
On groups covered by finitely many centralizers and domination number of the commuting graphs
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DOI: 10.1080/00927872.2019.1588977
Abstract: Abstract For a finite nonabelian group G, let be the smallest integer m such that G contains m proper centralizers with property In this article, we find for some groups of interest. For two isoclinic… read more here.
Keywords: domination number; finitely many; groups covered; many centralizers ... See more keywords
On the signed domination number of some Cayley graphs
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DOI: 10.1080/00927872.2020.1722830
Abstract: Abstract A signed dominating function of graph Γ is a function such that for each The signed domination number is the minimum weight of a signed dominating function on Γ. Let be a finite group… read more here.
Keywords: number cayley; domination number; signed domination; cayley graphs ... See more keywords