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An enterococcal phage-derived enzyme suppresses graft-versus-host disease. [PDF]
Fujimoto K +22 more
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Shallow shotgun metagenomic sequencing of vaginal microbiomes with the Oxford Nanopore technology enables the reliable determination of vaginal community state types and broad community structures. [PDF]
Graeber E +6 more
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Domination and Total Domination in Hypergraphs
2020A dominating set in a hypergraph H with vertex set V (H) and E(H) is a subset of vertices D ⊆ V (H) such that for every vertex v ∈ V (H) ∖ D, there exists an edge e ∈ E(H) for which v ∈ e and e ∩ D≠∅. A total dominating set in H is a dominating set D of H with the additional property that for every vertex v in D, there exists an edge e ∈ E(H) for which
Henning, Michael A., Yeo, Anders
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Domination and total domination in complementary prisms [PDF]
Let G be a graph and ${\overline {G}}$ be the complement of G. The complementary prism $G{\overline {G}}$ of G is the graph formed from the disjoint union of G and
Haynes, Teresa W. +2 more
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Quaestiones Mathematicae, 2015
A set S of vertices is a total dominating set of a graph G if every vertex of G is adjacent to some vertex in S. The minimum cardinality of a total dominating set is the total domination number γt(G). A Roman dominating function on a graph G is a function ƒ : V (G) → {0, 1, 2} satisfying the condition that every vertex u with ƒ(u) = 0 is adjacent to at
Chellali, Mustapha +2 more
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A set S of vertices is a total dominating set of a graph G if every vertex of G is adjacent to some vertex in S. The minimum cardinality of a total dominating set is the total domination number γt(G). A Roman dominating function on a graph G is a function ƒ : V (G) → {0, 1, 2} satisfying the condition that every vertex u with ƒ(u) = 0 is adjacent to at
Chellali, Mustapha +2 more
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Networks, 1980
AbstractA set D of vertices of a finite, undirected graph G = (V, E) is a total dominating set if every vertex of V is adjacent to some vertex of D. In this paper we initiate the study of total dominating sets in graphs and, in particular, obtain results concerning the total domination number of G (the smallest number of vertices in a total dominating ...
Ernest J. Cockayne +2 more
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AbstractA set D of vertices of a finite, undirected graph G = (V, E) is a total dominating set if every vertex of V is adjacent to some vertex of D. In this paper we initiate the study of total dominating sets in graphs and, in particular, obtain results concerning the total domination number of G (the smallest number of vertices in a total dominating ...
Ernest J. Cockayne +2 more
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Total Dominator Colorings and Total Domination in Graphs
Graphs and Combinatorics, 2014A total dominator coloring of a graph $$G$$G is a proper coloring of the vertices of $$G$$G in which each vertex of the graph is adjacent to every vertex of some color class. The total dominator chromatic number $$\chi _d^t(G)$$?dt(G) of $$G$$G is the minimum number of colors among all total dominator coloring of $$G$$G.
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