Results 11 to 20 of about 133,073 (208)
The general position problem and strong resolving graphs
Open Mathematics, 2019 The general position number gp(G) of a connected graph G is the cardinality of a largest set S of vertices such that no three pairwise distinct vertices from S lie on a common geodesic.
Klavžar Sandi, Yero Ismael G.
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Strong resolving graphs: The realization and the characterization problems
Discrete Applied Mathematics, 2018 arXiv admin note: text overlap with arXiv:1508 ...
Dorota Kuziak +3 more
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Strong resolving partitions for strong product graphs and Cartesian product graphs
Discrete Applied Mathematics, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Resolvability and Strong Resolvability in the Direct Product of Graphs [PDF]
Results in Mathematics, 2016 Given a connected graph $G$, a vertex $w\in V(G)$ distinguishes two different vertices $u,v$ of $G$ if the distances between $w$ and $u$ and between $w$ and $v$ are different. Moreover, $w$ strongly resolves the pair $u,v$ if there exists some shortest $u-w$ path containing $v$ or some shortest $v-w$ path containing $u$.
Dorota Kuziak +2 more
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Strong Resolving Hop Domination in Graphs
European Journal of Pure and Applied Mathematics, 2023 A vertex w in a connected graph G strongly resolves two distinct vertices u and v in V (G) if v is in any shortest u-w path or if u is in any shortest v-w path. A set W of vertices in G is a strong resolving set G if every two vertices of G are strongly resolved by some vertex of W.
Jerson Mohamad, Helen Rara
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On Movable Strong Resolving Domination in Graphs
European Journal of Pure and Applied Mathematics, 2022 Let G be a connected graph. A strong resolving dominating set S is a 1-movable strong resolving dominating set of G if for every v ∈ S, either S \ {v} is a strong resolving dominating set or there exists a vertex u ∈ (V (G) \ S) ∩ NG(v) such that (S \ {v}) ∪ {u} is a strong resolving dominating set of G.
Helyn Cosinas Sumaoy, Helen Rara
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Restrained Strong Resolving Hop Domination in Graphs
European Journal of Pure and Applied Mathematics, 2022 A set S ⊆ V (G) is a restrained strong resolving hop dominating set in G if for every v ∈ V (G)\S, there exists w ∈ S such that dG(v, w) = 2 and S = V (G) or V (G)\S has no isolated vertex. The smallest cardinality of such a set, denoted by γrsRh(G), is called the restrained strong resolving hop domination number of G.
Armalene Abragan, Helen Rara
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On Restrained Strong Resolving Domination in Graphs
European Journal of Pure and Applied Mathematics, 2021 A set S ⊆ V (G) is a restrained strong resolving dominating set in G if S is a strongresolving dominating set in G and S = V (G) or ⟨V (G) \ S⟩ has no isolated vertex. The restrained strong resolving domination number of G, denoted by γrsR(G), is the smallest cardinality of a restrained strong resolving dominating set in G.
Helyn Cosinas Sumaoy, Helen M. Rara
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General $d$-position sets [PDF]
, 2020 The general $d$-position number ${\rm gp}_d(G)$ of a graph $G$ is the cardinality of a largest set $S$ for which no three distinct vertices from $S$ lie on a common geodesic of length at most $d$.
Klavzar, Sandi +2 more
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On the resolving strong domination number of some wheel related graphs
Journal of Physics: Conference Series, 2022 Abstract This study aims to analyse the resolving strong dominating set. This concept combinations of two notions, they are metric dimension and strong domination set. By a resolving strong domination set, we mean a set D s ⊂ V(G) which satisfies the definition of strong dominating set as well as resolving set.
R Humaizah +4 more
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