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Upper distance-two domination [PDF]
Opuscula MathematicaLet \(G = (V, E)\) be a graph with vertex set \(V\) and edge set \(E\). A set \(S \subset V\) is a \(2\)-packing in \(G\) if for any two vertices \(u,v \in S\), the distance between them satisfies \(d(u,v) \gt 2\). The upper \(2\)-packing number \(P_2(G)\
Jason T. Hedetniemi +2 more
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Average distance and connected domination
AKCE International Journal of Graphs and Combinatorics, 2023 We give a tight upper bound on the average distance of a connected graph of given order in terms of its connected domination number. Our results are a strengthening of a result by DeLaViña, Pepper, and Waller [A note on dominating sets and average ...
P. Mafuta, S. Mukwembi
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Total $k$-distance domination critical graphs [PDF]
Transactions on Combinatorics, 2016 A set $S$ of vertices in a graph $G=(V,E)$ is called a total$k$-distance dominating set if every vertex in $V$ is withindistance $k$ of a vertex in $S$.
Doost Ali Mojdeh +3 more
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Exploring the properties of antituberculosis drugs through QSPR graph models and domination-based topological descriptors [PDF]
Scientific ReportsTuberculosis (TB) is a global health concern caused by the bacterium Mycobacterium tuberculosis. This infectious disease primarily affects the lungs but can also impact other organs.
Thilsath Parveen S +2 more
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Exploring the properties of benzenoid hydrocarbons through QSPR modeling and domination-based energy parameters [PDF]
Scientific ReportsThis article aims to explore two emerging areas of graph theory: chemical graph theory and domination theory. We specifically focus on a graph parameter that combines aspects of graph energy and domination, known as the dominating energy of a simple ...
Shanmugavelan Sankaran +1 more
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The Distance Roman Domination Numbers of Graphs
Discussiones Mathematicae Graph Theory, 2013 Let k be a positive integer, and let G be a simple graph with vertex set V (G). A k-distance Roman dominating function on G is a labeling f : V (G) → {0, 1, 2} such that for every vertex with label 0, there is a vertex with label 2 at distance at most k ...
Aram Hamideh +2 more
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Distance 2-Domination in Prisms of Graphs
Discussiones Mathematicae Graph Theory, 2017 A set of vertices D of a graph G is a distance 2-dominating set of G if the distance between each vertex u ∊ (V (G) − D) and D is at most two. Let γ2(G) denote the size of a smallest distance 2-dominating set of G. For any permutation π of the vertex set
Hurtado Ferran +3 more
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Universal distance domination in random graphs
Miskolc Mathematical NotesGiven a graph G=(V,E)D⊆VV∖DDGγ(G)GkDDdDk uk(G):= min {d:∀ D⊆V with |D|≥d,D is a kdd set in G}.kuk(G)γ(G)=u1(G)ukkkkH ...
Gábor Bacsó +2 more
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$k$-Efficient partitions of graphs [PDF]
Communications in Combinatorics and Optimization, 2019 A set $S = \{u_1,u_2, \ldots, u_t\}$ of vertices of $G$ is an efficient dominating set if every vertex of $G$ is dominated exactly once by the vertices of $S$.
M. Chellali +2 more
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Bounds On $(t,r)$ Broadcast Domination of $n$-Dimensional Grids [PDF]
Discrete Mathematics & Theoretical Computer Science, 2023 In this paper, we study a variant of graph domination known as $(t, r)$ broadcast domination, first defined in Blessing, Insko, Johnson, and Mauretour in 2015.
Tom Shlomi
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