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Relevant bibliographies by topics / Neighborhood total 2-domination

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Academic literature on the topic 'Neighborhood total 2-domination'

Author: Grafiati

Published: 3 June 2025

Last updated: 19 July 2025

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Journal articles on the topic "Neighborhood total 2-domination"

1

Lee, Chuan-Min. "Exploring Dominating Functions and Their Complexity in Subclasses of Weighted Chordal Graphs and Bipartite Graphs." Mathematics 13, no. 3 (2025): 403. https://doi.org/10.3390/math13030403.

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Domination problems are fundamental problems in graph theory with diverse applications in optimization, network design, and computational complexity. This paper investigates {k}-domination, k-tuple domination, and their total domination variants in weighted strongly chordal graphs and chordal bipartite graphs. Specifically, the {k}-domination problem in weighted strongly chordal graphs and the total {k}-domination problem in weighted chordal bipartite graphs are shown to be solvable in O(n+m) time. For weighted proper interval graphs and convex bipartite graphs, we solve the k-tuple domination

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2

Hassan, Javier, and Sergio R. Canoy, Jr. "Grundy Total Hop Dominating Sequences in Graphs." European Journal of Pure and Applied Mathematics 16, no. 4 (2023): 2597–612. http://dx.doi.org/10.29020/nybg.ejpam.v16i4.4877.

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Let G = (V (G), E(G)) be an undirected graph with γ(C) ̸= 1 for each component C of G. Let S = (v1, v2, · · · , vk) be a sequence of distint vertices of a graph G, and let Sˆ ={v1, v2, . . . , vk}. Then S is a legal open hop neighborhood sequence if N2G(vi) \Si−1j=1 N2G(vj ) ̸= ∅for every i ∈ {2, . . . , k}. If, in addition, Sˆ is a total hop dominating set of G, then S is a Grundy total hop dominating sequence. The maximum length of a Grundy total hop dominating sequence in a graph G, denoted by γth gr(G), is the Grundy total hop domination number of G. In this paper, we show that the Grundy

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3

C.Sivagnanam. "Neighborhood Total 2-Domination in Graphs." November 30, 2014. https://doi.org/10.5281/zenodo.826659.

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The graph G = (V,E) we mean a finite, undirected graph with neither loops nor multiple edges. The order and size of G are denoted by n and m respectively. For graph theoretic terminology we refer to Chartrand and Lesniak [3] and Haynes et.al [5-6].

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4

Chen, Qin. "Algorithm aspect on total Roman $\{2\}$-domination number of Cartesian products of paths and cycles." RAIRO - Operations Research, September 3, 2023. http://dx.doi.org/10.1051/ro/2023121.

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A total Roman $\{2\}$-dominating function (TR2DF) on a graph $G$ with vertex set $V$ is a function $f: V\rightarrow \{0,1,2\}$ having the property that for every vertex $v$ with $f(v)=0$, $\sum_{u\in N(v)}f(u)\geq 2$, where $N(v)$ represents the open neighborhood of $v$, and the subgraph of $G$ induced by the set of vertices with $f(v)>0$ has no isolated vertex. The weight of a TR2DF $f$ is the value $w(f)=\sum_{v\in V} f(v)$, and the minimum weight of a TR2DF of $G$ is the total Roman $\{2\}$-domination number $\gamma_{tR2}(G)$. The total Roman $\{2\}$-domination problem (TR2DP) is to dete

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5

Mahmoodi, Akram, Maryam Atapour, and Sepideh Norouzian. "On the signed strong total Roman domination number of graphs." Tamkang Journal of Mathematics, July 29, 2022. http://dx.doi.org/10.5556/j.tkjm.54.2023.3907.

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Let $G=(V,E)$ be a finite and simple graph of order $n$ and maximumdegree $\Delta$. A signed strong total Roman dominating function ona graph $G$ is a function $f:V(G)\rightarrow\{-1, 1,2,\ldots, \lceil\frac{\Delta}{2}\rceil+1\}$ satisfying the condition that (i) forevery vertex $v$ of $G$, $f(N(v))=\sum_{u\in N(v)}f(u)\geq 1$, where$N(v)$ is the open neighborhood of $v$ and (ii) every vertex $v$ forwhich $f(v)=-1$ is adjacent to at least one vertex$w$ for which $f(w)\geq 1+\lceil\frac{1}{2}\vert N(w)\cap V_{-1}\vert\rceil$, where$V_{-1}=\{v\in V: f(v)=-1\}$.The minimum of thevalues $\omega(f)

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6

Foucaud, Florent, and Michael A. Henning. "Locating-Total Dominating Sets in Twin-Free Graphs: a Conjecture." Electronic Journal of Combinatorics 23, no. 3 (2016). http://dx.doi.org/10.37236/5147.

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A total dominating set of a graph $G$ is a set $D$ of vertices of $G$ such that every vertex of $G$ has a neighbor in $D$. A locating-total dominating set of $G$ is a total dominating set $D$ of $G$ with the additional property that every two distinct vertices outside $D$ have distinct neighbors in $D$; that is, for distinct vertices $u$ and $v$ outside $D$, $N(u) \cap D \ne N(v) \cap D$ where $N(u)$ denotes the open neighborhood of $u$. A graph is twin-free if every two distinct vertices have distinct open and closed neighborhoods. The location-total domination number of $G$, denoted $\gamma_

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