Results 81 to 90 of about 7,293,468 (349)
Dominating Vertex Covers: The Vertex-Edge Domination Problem
Discussiones Mathematicae Graph Theory, 2021 The vertex-edge domination number of a graph, γve(G), is defined to be the cardinality of a smallest set D such that there exists a vertex cover C of G such that each vertex in C is dominated by a vertex in D.
Klostermeyer William F. +2 more
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Independent Dominating Set on Chain of Fuzzy Graphs
Tikrit Journal of Pure Science, 2023 In this paper, we applied some properties on chain fuzzy graphs, which comprise vertex identification. These properties are independent sets and independent dominant sets.
Russel H. Majeed, Nabeel E. Arif
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On graphs with disjoint dominating and 2-dominating sets [PDF]
Discussiones Mathematicae Graph Theory, 2013 A DD2-pair of a graph G is a pair (D,D2) of disjoint sets of vertices of G such that D is a dominating set and D2 is a 2-dominating set of G. Although there are infinitely many graphs that do not contain a DD2-pair, we show that every graph with minimum degree at least two has a DD2-pair.
Michael A. Henning, Douglas F. Rall
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Evolutionary interplay between viruses and R‐loops
FEBS Letters, EarlyView.Viruses interact with specialized nucleic acid structures called R‐loops to influence host transcription, epigenetic states, latency, and immune evasion. This Perspective examines the roles of R‐loops in viral replication, integration, and silencing, and how viruses co‐opt or avoid these structures.
Zsolt Karányi +4 more
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Bounds on the Locating-Domination Number and Differentiating-Total Domination Number in Trees
Discussiones Mathematicae Graph Theory, 2018 A subset S of vertices in a graph G = (V,E) is a dominating set of G if every vertex in V − S has a neighbor in S, and is a total dominating set if every vertex in V has a neighbor in S.
Rad Nader Jafari, Rahbani Hadi
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On Locating-Dominating Set of Regular Graphs
Journal of Mathematics, 2021 Let G be a simple, connected, and finite graph. For every vertex v∈VG, we denote by NGv the set of neighbours of v in G. The locating-dominating number of a graph G is defined as the minimum cardinality of W ⊆ VG such that every two distinct vertices u,v∈
Anuwar Kadir Abdul Gafur +1 more
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FEBS Letters, EarlyView.Exposure to common noxious agents (1), including allergens, pollutants, and micro‐nanoplastics, can cause epithelial barrier damage (2) in our body's protective linings. This may trigger an immune response to our microbiome (3). The epithelial barrier theory explains how this process can lead to chronic noncommunicable diseases (4) affecting organs ...
Can Zeyneloglu +17 more
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Augmenting graphs to partition their vertices into a total dominating set and an independent dominating set [PDF]
Opuscula MathematicaA graph \(G\) whose vertex set can be partitioned into a total dominating set and an independent dominating set is called a TI-graph. There exist infinite families of graphs that are not TI-graphs. We define the TI-augmentation number \(\operatorname{ti}(
Teresa W. Haynes, Michael A. Henning
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Results on Relatively Prime Domination Number of Vertex Switching of Some Graphs
Ratio Mathematica, 2023 If a set S ⊆ V has at least two members and every pair of vertices u and v is such that (d(u), d(v)) = 1, then it is said to be a relatively prime dominating set.
A Jancy Vini, C Jayasekaran
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On the number of minimum dominating sets and total dominating sets in forests
Journal of Graph TheoryAbstractWe show that the maximum number of minimum dominating sets of a forest with domination number is at most and construct for each a tree with domination number that has more than minimum dominating sets. Furthermore, we disprove a conjecture about the number of minimum total dominating sets in forests by Henning, Mohr and Rautenbach.
Jan Petr, Julien Portier, Leo Versteegen
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