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Journal articles on the topic 'Locating sets'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Jean, Devin C., and Suk J. Seo. "Error-correcting open-locating-dominating sets." Congressus Numerantium 235 (January 11, 2025): 23–40. https://doi.org/10.61091/cn235-03.

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An open-locating-dominating set of a graph models a detection system for a facility with a possible “intruder” or a multiprocessor network with a possible malfunctioning processor. A “sensor” or “detector” is assumed to be installed at a subset of vertices where each can detect an intruder or a malfunctioning processor in its neighborhood, but not at its own location. We consider a fault-tolerant variant of an open-locating-dominating set called an error-correcting open-locating-dominating set, which can correct a false-positive or a false-negative signal from a detector. In particular, we pro

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2

Canoy, Jr., Sergio R., Gina A. Malacas, and Dennis Tarepe. "Locating dominating sets in graphs." Applied Mathematical Sciences 8 (2014): 4381–88. http://dx.doi.org/10.12988/ams.2014.46400.

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3

Omega, Stephanie A., and Sergio R. Canoy, Jr. "Locating sets in a graph." Applied Mathematical Sciences 9 (2015): 2957–64. http://dx.doi.org/10.12988/ams.2015.5291.

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4

Slater, Peter J. "Fault-tolerant locating-dominating sets." Discrete Mathematics 249, no. 1-3 (2002): 179–89. http://dx.doi.org/10.1016/s0012-365x(01)00244-8.

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5

Murtaza, Muhammad, Muhammad Fazil, and Imran Javaid. "Locating-dominating sets of functigraphs." Theoretical Computer Science 799 (December 2019): 115–23. http://dx.doi.org/10.1016/j.tcs.2019.09.051.

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6

Jean, Devin C., and Suk J. Seo. "On redundant locating-dominating sets." Discrete Applied Mathematics 329 (April 2023): 106–25. http://dx.doi.org/10.1016/j.dam.2023.01.023.

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7

Fazil, Muhammad, Imran Javaid, Muhammad Salman, and Usman Ali. "Locating-dominating sets in hypergraphs." Periodica Mathematica Hungarica 72, no. 2 (2016): 224–34. http://dx.doi.org/10.1007/s10998-016-0121-8.

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8

Ahmad, Eman Camad, Gina Alquiza Malacas, and Sergio Jr Rosales Canoy. "Stable Locating-Dominating Sets in Graphs." European Journal of Pure and Applied Mathematics 14, no. 3 (2021): 638–49. http://dx.doi.org/10.29020/nybg.ejpam.v14i3.3998.

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A set S âŠ† V(G) of a (simple) undirected graph G is a locating-dominating set of G if for each v âˆˆ V(G) \ S, there exists w âˆˆ S such tha vw âˆˆ E(G) and NG(x) âˆ© S= NG(y)âˆ©S for any distinct vertices x and y in V(G) \ S. S is a stable locating-dominating set of G if it is a locating-dominating set of G and S \ {v} is a locating-dominating set of G for each v âˆˆ S. The minimum cardinality of a stable locating-dominating set of G, denoted by Î³sl(G), is called the stable locating-domination number of G. In this paper, we investigate this concept and the corresponding parameter for some g

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9

Pagcu, Ethel Mae, Gina Malacas, and Sergio Canoy, Jr. "Locating Hop Sets in a Graph." European Journal of Pure and Applied Mathematics 15, no. 4 (2022): 1705–15. http://dx.doi.org/10.29020/nybg.ejpam.v15i4.4500.

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Let G be a connected graph with vertex set V (G) and edge set E(G). The open hop neighborhood of vertex v ∈ V (G) is the set NG(v, 2) = {w ∈ V (G) : dG(v, w) = 2}, where dG(v, w) denotes the distance between v and w. A non-empty set S ⊆ V (G) is a locating hop set of G if NG(u, 2) ∩ S ̸= NG(v, 2) ∩ S for every pair of distinct vertices u, v ∈ V (G) \ S. The smallest cardinality of a locating hop set of G, denoted by lhn(G) is called the locating hop number of G. This study focuses mainly on the concept of locating hop set in graphs. Characterizations of locating hop sets in the join and corona

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10

Tropico, Irish S., and Isagani S. Cabahug, Jr. "Internally-Locating Dominating Sets in Graphs." European Journal of Pure and Applied Mathematics 18, no. 2 (2025): 5918. https://doi.org/10.29020/nybg.ejpam.v18i2.5918.

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For a connected graph \( G \), a subset \( I \subseteq V(G) \) is a locating-dominating set if it is a dominating set and for every two distinct vertices \( x, y \in V(G) \setminus I \), \( N(x) \cap I \neq N(y) \cap I \). This paper introduces the concept of an internally-locating dominating set. Specifically, a nonempty set \( I \subseteq V(G) \) with \( |I| \geq 2 \) is an internally-locating set in a nontrivial connected graph \( G \) if and only if, for every \( u, v \in I \), \( N(u) \cap I \neq N(v) \cap I \). Thus, \( I \) is an internally-locating dominating set if it is both an inter

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11

Canete, Gymaima, Helen Rara, and Angelica Mae Mahistrado. "2-Locating Sets in a Graph." European Journal of Pure and Applied Mathematics 16, no. 3 (2023): 1647–62. http://dx.doi.org/10.29020/nybg.ejpam.v16i3.4821.

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Let $G$ be an undirected graph with vertex-set $V(G)$ and edge-set $E(G)$, respectively. A set $S\subseteq V(G)$ is a $2$-locating set of $G$ if $\big|[\big(N_G(x)\backslash N_G(y)\big)\cap S] \cup [\big(N_G(y)\backslash N_G(x)\big)\cap S]\big|\geq 2$, for all \linebreak $x,y\in V(G)\backslash S$ with $x\neq y$, and for all $v\in S$ and $w\in V(G)\backslash S$, $\big(N_G(v)\backslash N_G(w)\big)\cap S \neq \varnothing$ or $\big(N_G(w)\backslash N_G[v]\big) \cap S\neq \varnothing$. In this paper, we investigate the concept and study 2-locating sets in graphs resulting from some binary operation

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12

Cappelle, Márcia R., Guilherme C. M. Gomes, and Vinicius F. dos Santos. "Parameterized algorithms for locating-dominating sets." Procedia Computer Science 195 (2021): 68–76. http://dx.doi.org/10.1016/j.procs.2021.11.012.

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13

Seo, Suk J., and Peter J. Slater. "Open-independent, open-locating-dominating sets." Electronic Journal of Graph Theory and Applications 5, no. 2 (2017): 179–93. http://dx.doi.org/10.5614/ejgta.2017.5.2.2.

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14

Hernández, Elvira, and Luis Rodríguez-Marín. "Locating minimal sets using polyhedral cones." Operations Research Letters 39, no. 6 (2011): 466–70. http://dx.doi.org/10.1016/j.orl.2011.08.004.

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15

Lloyd, Errol L., Mary Lou Soffa, and Ching-Chy Wang. "On locating minimum feedback vertex sets." Journal of Computer and System Sciences 37, no. 3 (1988): 292–311. http://dx.doi.org/10.1016/0022-0000(88)90009-8.

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16

Bellitto, Thomas, Caroline Brosse, Benjamin Lévêque, and Aline Parreau. "Locating-dominating sets in local tournaments." Discrete Applied Mathematics 337 (October 2023): 14–24. http://dx.doi.org/10.1016/j.dam.2023.04.010.

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17

Arsie, Alessandro, and Christian Ebenbauer. "Locating omega-limit sets using height functions." Journal of Differential Equations 248, no. 10 (2010): 2458–69. http://dx.doi.org/10.1016/j.jde.2009.11.012.

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18

Haynes, Teresa W., Michael A. Henning, and Jamie Howard. "Locating and total dominating sets in trees." Discrete Applied Mathematics 154, no. 8 (2006): 1293–300. http://dx.doi.org/10.1016/j.dam.2006.01.002.

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19

McCoy, John, and Michael A. Henning. "Locating and paired-dominating sets in graphs." Discrete Applied Mathematics 157, no. 15 (2009): 3268–80. http://dx.doi.org/10.1016/j.dam.2009.06.019.

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20

Niepel, Ľudovít. "Locating–paired-dominating sets in square grids." Discrete Mathematics 338, no. 10 (2015): 1699–705. http://dx.doi.org/10.1016/j.disc.2014.07.009.

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21

Honkala, Iiro, and Tero Laihonen. "On locating–dominating sets in infinite grids." European Journal of Combinatorics 27, no. 2 (2006): 218–27. http://dx.doi.org/10.1016/j.ejc.2004.09.002.

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22

Honkala, Iiro. "On r-locating–dominating sets in paths." European Journal of Combinatorics 30, no. 4 (2009): 1022–25. http://dx.doi.org/10.1016/j.ejc.2008.04.011.

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23

Foucaud, Florent, Michael A. Henning, Christian Löwenstein, and Thomas Sasse. "Locating–dominating sets in twin-free graphs." Discrete Applied Mathematics 200 (February 2016): 52–58. http://dx.doi.org/10.1016/j.dam.2015.06.038.

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24

Faudree, Ralph J., Hao Li, and Kiyoshi Yoshimoto. "Locating sets of vertices on Hamiltonian cycles." Discrete Applied Mathematics 209 (August 2016): 107–14. http://dx.doi.org/10.1016/j.dam.2015.11.012.

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25

Pirzada, S., Rameez Raja, and Shane Redmond. "Locating sets and numbers of graphs associated to commutative rings." Journal of Algebra and Its Applications 13, no. 07 (2014): 1450047. http://dx.doi.org/10.1142/s0219498814500479.

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For a graph G(V, E) with order n ≥ 2, the locating code of a vertex v is a finite vector representing distances of v with respect to vertices of some ordered subset W of V(G). The set W is a locating set of G(V, E) if distinct vertices have distinct codes. A locating set containing a minimum number of vertices is a minimum locating set for G(V, E). The locating number denoted by loc (G) is the number of vertices in the minimum locating set. Let R be a commutative ring with identity 1 ≠ 0, the zero-divisor graph denoted by Γ(R), is the (undirected) graph whose vertices are the nonzero zero-divi

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26

Raza, Hassan, Sakander Hayat, and Xiang-Feng Pan. "Binary Locating-Dominating Sets in Rotationally-Symmetric Convex Polytopes." Symmetry 10, no. 12 (2018): 727. http://dx.doi.org/10.3390/sym10120727.

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A convex polytope or simply polytope is the convex hull of a finite set of points in Euclidean space R d . Graphs of convex polytopes emerge from geometric structures of convex polytopes by preserving the adjacency-incidence relation between vertices. In this paper, we study the problem of binary locating-dominating number for the graphs of convex polytopes which are symmetric rotationally. We provide an integer linear programming (ILP) formulation for the binary locating-dominating problem of graphs. We have determined the exact values of the binary locating-dominating number for two infinite

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27

Murtaza, M., I. Javaid, and M. Fazil. "Covering codes of a graph associated to a finite vector space." Ukrains’kyi Matematychnyi Zhurnal 72, no. 7 (2020): 952–59. http://dx.doi.org/10.37863/umzh.v72i7.652.

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UDC 512.5 In this paper, we investigate the problem of covering the vertices of a graph associated to a finite vector space as introduced by Das [Commun. Algebra, <strong>44</strong>, 3918 – 3926 (2016)], such that we can uniquely identify any vertex by examining the vertices that cover it. We use locating-dominating sets and identifying codes, which are closely related concepts for this purpose. We find the location-domination number and the identifying number of the graph and study the exchange property for locating-dominating sets and identifying codes.

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28

Bousquet, Nicolas, Quentin Deschamps, Tuomo Lehtilä, and Aline Parreau. "Locating-dominating sets: From graphs to oriented graphs." Discrete Mathematics 346, no. 1 (2023): 113124. http://dx.doi.org/10.1016/j.disc.2022.113124.

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29

Chinneck, John W., and Erik W. Dravnieks. "Locating Minimal Infeasible Constraint Sets in Linear Programs." ORSA Journal on Computing 3, no. 2 (1991): 157–68. http://dx.doi.org/10.1287/ijoc.3.2.157.

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30

Malacas, Gina A., Sergio Canoy, Jr., and Emmy Chacon. "Stable Locating-Dominating Sets in the Edge Corona and Lexicographic Product of Graphs." European Journal of Pure and Applied Mathematics 16, no. 1 (2023): 479–90. http://dx.doi.org/10.29020/nybg.ejpam.v16i1.4645.

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A set S ⊆ V (G) of an undirected graph G is a locating-dominating set of G if for each v ∈ V (G) \ S, there exists w ∈ S such tha vw ∈ E(G) and NG(x) ∩ S ̸= NG(y) ∩ S for any two distinct vertices x and y in V (G) \ S. S is a stable locating-dominating set of G if it is a locating-dominating set of G and S \ {v} is a locating-dominating set of G for each v ∈ S. The minimum cardinality of a stable locating-dominating set of G, denoted by γSLD(G), is called the stable locating-domination number of G. In this paper, we investigate this concept and the corresponding parameter for edge corona and l

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31

French, Brian F., and W. Holmes Finch. "Multigroup Confirmatory Factor Analysis: Locating the Invariant Referent Sets." Structural Equation Modeling: A Multidisciplinary Journal 15, no. 1 (2008): 96–113. http://dx.doi.org/10.1080/10705510701758349.

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32

Argiroffo, Gabriela R., Silvia M. Bianchi, and Annegret K. Wagler. "A polyhedral approach to locating-dominating sets in graphs." Electronic Notes in Discrete Mathematics 50 (December 2015): 89–94. http://dx.doi.org/10.1016/j.endm.2015.07.016.

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33

Kincaid, Rex, Allison Oldham, and Gexin Yu. "Optimal open-locating-dominating sets in infinite triangular grids." Discrete Applied Mathematics 193 (October 2015): 139–44. http://dx.doi.org/10.1016/j.dam.2015.04.024.

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34

Ortega, Marivir, Gina Malacas, and Sergio R. Canoy, Jr. "Global Stable Location-Domination in Graphs." European Journal of Pure and Applied Mathematics 16, no. 3 (2023): 1685–94. http://dx.doi.org/10.29020/nybg.ejpam.v16i3.4748.

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In this paper, we introduce and investigate the concept of global stable location-domination in graphs. We also characterize the global stable locating-dominating sets in the join, edge corona, corona, and lexicographic product of graphs and determine the exact value or sharp bound of the corresponding global stable location-domination number.

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35

Junnila, Ville. "Optimal locating-total dominating sets in strips of height 3." Discussiones Mathematicae Graph Theory 35, no. 3 (2015): 447. http://dx.doi.org/10.7151/dmgt.1805.

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36

Bousquet, Nicolas, Quentin Chuet, Victor Falgas–Ravry, Amaury Jacques, and Laure Morelle. "A note on locating-dominating sets in twin-free graphs." Discrete Mathematics 348, no. 2 (2025): 114297. http://dx.doi.org/10.1016/j.disc.2024.114297.

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37

Cappelle, Márcia R., Erika M. M. Coelho, Les R. Foulds, and Humberto J. Longo. "Open-independent, Open-locating-dominating Sets in Complementary Prism Graphs." Electronic Notes in Theoretical Computer Science 346 (August 2019): 253–64. http://dx.doi.org/10.1016/j.entcs.2019.08.023.

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38

Froyland, Gary, and Michael Dellnitz. "Detecting and Locating Near-Optimal Almost-Invariant Sets and Cycles." SIAM Journal on Scientific Computing 24, no. 6 (2003): 1839–63. http://dx.doi.org/10.1137/s106482750238911x.

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39

Chen, Chunxia, Changhong Lu, and Zhengke Miao. "Identifying codes and locating–dominating sets on paths and cycles." Discrete Applied Mathematics 159, no. 15 (2011): 1540–47. http://dx.doi.org/10.1016/j.dam.2011.06.008.

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40

Wang, Zhongqi, Yuan Yang, Bo Yang, and Yonggang Kang. "Optimal sheet metal fixture locating layout by combining radial basis function neural network and bat algorithm." Advances in Mechanical Engineering 8, no. 12 (2016): 168781401668190. http://dx.doi.org/10.1177/1687814016681905.

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Considering that sheet metal part has the properties of thin wall, low rigidity, easy to deform, and difficult to locate, this article proposes a new approach to optimizing sheet metal fixture locating layout by combining radial basis function neural network and bat algorithm. First, taking fixture locating layout as design variables based on the “ N-2-1” locating principle, this article generates limited training and testing sample sets by Latin hypercube sampling and finite element analysis. Second, the radial basis function neural network prediction model with the description of the nonline

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41

Kathiresan, KM, and S. Jeyagermani. "Multiplicative Distance-Location Number of Graphs." Utilitas Mathematica 120, no. 1 (2024): 27–36. http://dx.doi.org/10.61091/um120-04.

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For a set \( S \) of vertices in a connected graph \( G \), the multiplicative distance of a vertex \( v \) with respect to \( S \) is defined by \(d_{S}^{*}(v) = \prod\limits_{x \in S, x \neq v} d(v,x).\) If \( d_{S}^{*}(u) \neq d_{S}^{*}(v) \) for each pair \( u,v \) of distinct vertices of \( G \), then \( S \) is called a multiplicative distance-locating set of \( G \). The minimum cardinality of a multiplicative distance-locating set of \( G \) is called its multiplicative distance-location number \( loc_{d}^{*}(G) \). If \( d_{S}^{*}(u) \neq d_{S}^{*}(v) \) for each pair \( u,v \) of dis

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42

Chakraborty, Dipayan, Florent Foucaud, Anni Hakanen, Michael A. Henning, and Annegret K. Wagler. "Progress towards the two-thirds conjecture on locating-total dominating sets." Discrete Mathematics 347, no. 12 (2024): 114176. http://dx.doi.org/10.1016/j.disc.2024.114176.

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43

Csendes, Tibor, and János Pintér. "A new interval method for locating the boundary of level sets." International Journal of Computer Mathematics 49, no. 1-2 (1993): 53–59. http://dx.doi.org/10.1080/00207169308804215.

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44

Slater, Mark. "Locating Project Studios and Studio Projects." Journal of the Royal Musical Association 141, no. 1 (2016): 167–202. http://dx.doi.org/10.1080/02690403.2016.1151241.

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ABSTRACTVia a longitudinal case study of a studio project (Middlewood Sessions, 2004–12), this research explores processes of music-making in the increasingly prevalent context of the project studio to give an insight into contemporary music-making practices. Predicated upon technologies of decreasing size but increasing processing power, project studios represent a diversification of musical creativity in terms of the persons and locations of music production. Increasingly mobile technologies lead to increasingly mobile practices of music production, which presents a challenge to the seemingl

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45

Teodorović, Dušan, and Milica Šelmić. "LOCATING FLOW-CAPTURING FACILITIES IN TRANSPORTATION NETWORKS: A FUZZY SETS THEORY APPROACH." International Journal for Traffic and Transport Engineering 3, no. 2 (2013): 103–11. http://dx.doi.org/10.7708/ijtte.2013.3(2).01.

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46

Omamalin, Benjamin N., Sergio R. Canoy, Jr., and Helen M. Rara. "Locating total dominating sets in the join, corona and composition of graphs." Applied Mathematical Sciences 8 (2014): 2363–74. http://dx.doi.org/10.12988/ams.2014.43205.

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47

González, Antonio, Carmen Hernando, and Mercè Mora. "Metric-locating-dominating sets of graphs for constructing related subsets of vertices." Applied Mathematics and Computation 332 (September 2018): 449–56. http://dx.doi.org/10.1016/j.amc.2018.03.053.

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48

Fathali, Jafar, and Ali Jamalian. "Locating Multiple Facilities in Convex Sets with Fuzzy Data and Block Norms." Applied Mathematics 03, no. 12 (2012): 1950–58. http://dx.doi.org/10.4236/am.2012.312267.

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49

Wang, Jonathan, Kesheng Wu, Alex Sim, and Seongwook Hwangbo. "Locating Partial Discharges in Power Transformers with Convolutional Iterative Filtering." Sensors 23, no. 4 (2023): 1789. http://dx.doi.org/10.3390/s23041789.

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The most common source of transformer failure is in the insulation, and the most prevalent warning signal for insulation weakness is partial discharge (PD). Locating the positions of these partial discharges would help repair the transformer to prevent failures. This work investigates algorithms that could be deployed to locate the position of a PD event using data from ultra-high frequency (UHF) sensors inside the transformer. These algorithms typically proceed in two steps: first determining the signal arrival time, and then locating the position based on time differences. This paper reviews

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50

Raja, Rameez, S. Pirzada, and Shane Redmond. "On locating numbers and codes of zero divisor graphs associated with commutative rings." Journal of Algebra and Its Applications 15, no. 01 (2015): 1650014. http://dx.doi.org/10.1142/s0219498816500146.

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Let R be a commutative ring with identity and let G(V, E) be a graph. The locating number of the graph G(V, E) denoted by loc (G) is the cardinality of the minimal locating set W ⊆ V(G). To get the loc (G), we assign locating codes to the vertices V(G)∖W of G in such a way that every two vertices get different codes. In this paper, we consider the ratio of loc (G) to |V(G)| and show that there is a finite connected graph G with loc (G)/|V(G)| = m/n, where m < n are positive integers. We examine two equivalence relations on the vertices of Γ(R) and the relationship between locating sets and

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