Results 11 to 20 of about 5,633 (238)
Distance Domination and Distance Irredundance in Graphs [PDF]
The Electronic Journal of Combinatorics, 2007 A set $D\subseteq V$ of vertices is said to be a (connected) distance $k$-dominating set of $G$ if the distance between each vertex $u\in V-D$ and $D$ is at most $k$ (and $D$ induces a connected graph in $G$). The minimum cardinality of a (connected) distance $k$-dominating set in $G$ is the (connected) distance $k$-domination number of $G$, denoted ...
Hansberg, Adriana +2 more
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Semipaired Domination in Some Subclasses of Chordal Graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 A dominating set $D$ of a graph $G$ without isolated vertices is called semipaired dominating set if $D$ can be partitioned into $2$-element subsets such that the vertices in each set are at distance at most $2$. The semipaired domination number, denoted
Michael A. Henning +2 more
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Eternal Distance-k Domination on Graphs
La Matematica, 2023 Eternal domination is a dynamic process by which a graph is protected from an infinite sequence of vertex intrusions. In eternal distance-$k$ domination, guards initially occupy the vertices of a distance-$k$ dominating set. After a vertex is attacked, guards ``defend'' by each moving up to distance $k$ to form a distance-$k$ dominating set, such that ...
D. Cox, E. Meger, M. E. Messinger
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Superior domination polynomial of cycles
Ratio Mathematica, 2023 Superior domination polynomial SD(G, x) is a polynomial in which the power of the variable denotes the cardinality of a superior dominating set and the total number of sets of same cardinality forms the coefficient of the variable.
R Tejaskumar
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Semitotal domination in trees [PDF]
Discrete Mathematics & Theoretical Computer Science, 2018 In this paper, we study a parameter that is squeezed between arguably the two important domination parameters, namely the domination number, $\gamma(G)$, and the total domination number, $\gamma_t(G)$.
Zhuang Wei, Hao Guoliang
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On the distance domination number of bipartite graphs
Electronic Journal of Graph Theory and Applications, 2020 A subset D ⊆ V(G) is called a k-distance dominating set of G if every vertex in V(G)-D is within distance k from some vertex of D. The minimum cardinality among all k-distance dominating sets of G is called the k-distance domination number of G.
Doost Ali Mojdeh +2 more
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Distance Domination in Vertex Partitioned Graphs
Mathematica Pannonica, 2022 We treat a variation of graph domination which involves a partition (V 1, V 2,..., Vk) of the vertex set of a graph G and domination of each partition class V i over distance d where all vertices and edges of G may be used in the domination process. Strict upper bounds and extremal graphs are presented; the results are collected in three handy tables ...
Frendrup, Allan +2 more
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Distance domination versus iterated domination
Discrete Mathematics, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bacsó, Gábor, Tuza, Zsolt
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JTAM (Jurnal Teori dan Aplikasi Matematika), 2022 The study purpose is to determine the four-distance domination number in the amalgamation operation graph, namely the vertex amalgamation result graph of ladder graph Amal(L_m,v,n) with m≥2 and n≥2 and the vertex amalgamation result graph of a star graph
Ilham Saifudin +2 more
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Electronic Notes in Discrete Mathematics, 2013 For any graph G=(V,E), a subset S⊆V dominates G if all vertices are contained in the closed neighborhood of S, that is N[S]=V. The minimum cardinality over all such S is called the domination number, written γ(G). For any positive integer k, a general k-distance domination function of a graph G is a function f:V→{0,1,…,k} such that every vertex with ...
Elliot Krop, Tony Yaacoub
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