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Journal articles on the topic 'Locating number'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

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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P, Anagha, and Sameena K. "Locating number of a tree." Malaya Journal of Matematik S, no. 1 (2019): 472–75. http://dx.doi.org/10.26637/mjm0s01/0084.

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Damayanti, M., Asmiati, Fitriani, M. Ansori, and A. Faradilla. "The Locating Chromatic Number of some Modified Path with Cycle having Locating Number Four." Journal of Physics: Conference Series 1751 (January 2021): 012008. http://dx.doi.org/10.1088/1742-6596/1751/1/012008.

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Irawan, Agus, Asmiati Asmiati, La Zakaria, and Kurnia Muludi. "The Locating-Chromatic Number of Origami Graphs." Algorithms 14, no. 6 (2021): 167. http://dx.doi.org/10.3390/a14060167.

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The locating-chromatic number of a graph combines two graph concepts, namely coloring vertices and partition dimension of a graph. The locating-chromatic number is the smallest k such that G has a locating k-coloring, denoted by χL(G). This article proposes a procedure for obtaining a locating-chromatic number for an origami graph and its subdivision (one vertex on an outer edge) through two theorems with proofs.

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Syofyan, Dian Kastika, Edy Tri Baskoro, and Hilda Assiyatun. "Trees with Certain Locating-Chromatic Number." Journal of Mathematical and Fundamental Sciences 48, no. 1 (2016): 39–47. http://dx.doi.org/10.5614/j.math.fund.sci.2016.48.1.4.

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6

Asmiati. "Locating chromatic number of banana tree." International Mathematical Forum 12 (2017): 39–45. http://dx.doi.org/10.12988/imf.2017.610138.

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Inayah, Nur, Wisnu Aribowo, and Maiyudi Mariska Windra Yahya. "The Locating Chromatic Number of Book Graph." Journal of Mathematics 2021 (November 24, 2021): 1–3. http://dx.doi.org/10.1155/2021/3716361.

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Let G = V G , E G be a connected graph and c : V G ⟶ 1,2 , … , k be a proper k -coloring of G . Let Π be a partition of vertices of G induced by the coloring c . We define the color code c Π v of a vertex v ∈ V G as an ordered k -tuple that contains the distance between each partition to the vertex v . If distinct vertices have distinct color code, then c is called a locating k -coloring of G . The locating chromatic number of G is the smallest k such that G has a locating k -coloring. In this paper, we determine the locating chromatic number of book graph.

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Zafar, Hassan, Muhammad Javaid, and Ebenezer Bonyah. "Local Fractional Locating Number of Convex Polytope Networks." Mathematical Problems in Engineering 2022 (September 27, 2022): 1–14. http://dx.doi.org/10.1155/2022/3723427.

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The concept of locating number for a connected network contributes an important role in computer networking, loran and sonar models, integer programming and formation of chemical structures. In particular it is used in robot navigation to control the orientation and position of robot in a network, where the places of navigating agents can be replaced with the vertices of a network. In this note, we have studied the latest invariant of locating number known as local fractional locating number of an antiprism based convex polytope networks. Furthermore, it is also proved that these convex polyto

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Wei, Jianxin, Uzma Ahmad, Saira Hameed, and Javaria Hanif. "Locating-Total Domination Number of Cacti Graphs." Mathematical Problems in Engineering 2020 (October 18, 2020): 1–10. http://dx.doi.org/10.1155/2020/6197065.

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For a connected graph J, a subset W ⊆ V J is termed as a locating-total dominating set if for a ∈ V J , N a ∩ W ≠ ϕ , and for a , b ∈ V J − W , N a ∩ W ≠ N b ∩ W . The number of elements in a smallest such subset is termed as the locating-total domination number of J. In this paper, the locating-total domination number of unicyclic graphs and bicyclic graphs are studied and their bounds are presented. Then, by using these bounds, an upper bound for cacti graphs in terms of their order and number of cycles is estimated. Moreover, the exact values of this domination variant for some families of

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10

Arfin, Arfin. "The Locating-Chromatic Number of Some Jellyfish Graphs." Journal of the Indonesian Mathematical Society 31, no. 1 (2025): 1627. https://doi.org/10.22342/jims.v31i1.1627.

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Let c be a proper coloring of a graph G = (V, E) with k colors which induces a partition Π of V (G) into color classes L1, L2, . . . , Lk . For each vertex v in G, the color code cΠ(v) is defined as the ordered k-tuple (d(v, L1), d(v, L2), . . . , d(v, Lk )), where d(v, Li) represents the minimum distance from v to all other vertices u in Li(1 ≤ i ≤ k). If every vertex possesses unique color codes, then c is called a locating-k-coloring in G. If k is the minimum number such that c is a locating-k-coloring in G, then the locating-chromatic number of G is χL(G) = k. In this paper, the author det

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11

Rajasekar, G., K. Nagarajan, and M. Seenivasan. "Location Domination Number of Sum of Graphs." International Journal of Engineering & Technology 7, no. 4.10 (2018): 852. http://dx.doi.org/10.14419/ijet.v7i4.10.26774.

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Locating dominating set is the subset of the vertex set which dominate and uniquely identify all vertices of the set . In this paper we formulated the apt method for finding the location domination number of sum of graphs based on the nature of the graphs and .

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Sakri, Redha, and Moncef Abbas. "On locating chromatic number of Möbius ladder graphs." Proyecciones (Antofagasta) 40, no. 3 (2021): 659–69. http://dx.doi.org/10.22199/issn.0717-6279-4170.

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13

Takatsuka, Hiroki, Seiki Tokunaga, Sachio Saiki, Shinsuke Matsumoto, and Masahide Nakamura. "KULOCS: unified locating service for efficient development of location-based applications." International Journal of Pervasive Computing and Communications 12, no. 1 (2016): 154–72. http://dx.doi.org/10.1108/ijpcc-01-2016-0004.

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Purpose The purpose of this paper is to develop a facade for seamlessly using locating services and enabling easy development of an application with indoor and outdoor location information without being aware of the difference of individual services. To achieve this purpose, in this paper, a unified locating service, called KULOCS (Kobe-University Unified LOCating Service), which horizontally integrates the heterogeneous locating services, is proposed. Design/methodology/approach By focusing on technology-independent elements [when], [where] and [who] in location queries, KULOCS integrates dat

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Welyyanti, D., M. Azhari, and R. Lestari. "On Locating Chromatic Number of Disconnected Graph." Journal of Physics: Conference Series 1940, no. 1 (2021): 012019. http://dx.doi.org/10.1088/1742-6596/1940/1/012019.

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Asmiati, H. Assiyatun, and E. T. Baskoro. "Locating-Chromatic Number of Amalgamation of Stars." ITB Journal of Sciences 43, no. 1 (2011): 1–8. http://dx.doi.org/10.5614/itbj.sci.2011.43.1.1.

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Hamdi, Muhammad, Des Welyyanti, and Ikhlas Pratama Sandy. "LOCATING CHROMATIC NUMBER OF ONE-HEART GRAPH." Jurnal Matematika UNAND 14, no. 1 (2025): 85. https://doi.org/10.25077/jmua.14.1.85-92.2025.

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Bilangan kromatik lokasi merupakan konsep dari dimensi partisi graf dengan pewarnaan titik graf. Bilangan kromatik lokasi dari G, dinotasikan dengan χL(G) adalah jumlah warna minimum yang dipakai untuk pewarnaan lokasi. Dalam Artikel ini dijelaskan cara menentukan bilangan kromatik lokasi graf sehati. Metode yang dipakai agar diperolehnya bilangan kromatik lokasi graf sehati adalah dengan memperoleh nilai eksaknya. Hasil yang didapatkan dari bilangan kromatik lokasi graf sehati adalah χL(Hr_n)=4 untuk n=2 dan χL(Hr_n)=5 untuk n≥3.

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17

Syofyan, Dian Kastika, Edy Tri Baskoro, and Hilda Assiyatun. "The Locating-Chromatic Number of Binary Trees." Procedia Computer Science 74 (2015): 79–83. http://dx.doi.org/10.1016/j.procs.2015.12.079.

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18

Surbakti, Nurul Maulida, Dinda Kartika, Hamidah Nasution, and Sri Dewi. "The Locating Chromatic Number for Pizza Graphs." Sainmatika: Jurnal Ilmiah Matematika dan Ilmu Pengetahuan Alam 20, no. 2 (2023): 126–31. http://dx.doi.org/10.31851/sainmatika.v20i2.13085.

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The location chromatic number for a graph is an extension of the concepts of partition dimension and vertex coloring in a graph. The minimum number of colors required to perform location coloring in graph G is referred to as the location chromatic number of graph G. This research is a literature study that discusses the location chromatic number of the Pizza graph. The approach used to calculate the location-chromatic number of these graphs involves determining upper and lower bounds. The results obtained show that the location chromatic number of the pizza graph is 4 for n = 3 and n for ≥ 4.

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19

Azeem, Muhammad, Muhammad Kamran Jamil, and Yilun Shang. "Notes on the Localization of Generalized Hexagonal Cellular Networks." Mathematics 11, no. 4 (2023): 844. http://dx.doi.org/10.3390/math11040844.

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The act of accessing the exact location, or position, of a node in a network is known as the localization of a network. In this methodology, the precise location of each node within a network can be made in the terms of certain chosen nodes in a subset. This subset is known as the locating set and its minimum cardinality is called the locating number of a network. The generalized hexagonal cellular network is a novel structure for the planning and analysis of a network. In this work, we considered conducting the localization of a generalized hexagonal cellular network. Moreover, we determined

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20

Fran, Fransiskus, Elishabet Yohana, and Yundari Yundari. "BILANGAN DOMINASI LOKASI PADA LINE PAN GRAPH DAN MIDDLE PAN GRAPH." EduMatSains : Jurnal Pendidikan, Matematika dan Sains 6, no. 1 (2021): 61–70. http://dx.doi.org/10.33541/edumatsains.v6i1.2928.

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Let G is a simple, connected, and undirected graph. A set D is a subset of V. If every node of V adjacent to at least one node D, then D is a dominating set of the graph G . One of the topics from dominating set is locating dominating set. Locating dominating set is dominating set on condition if every two vertices u,v elements of V-D satisfy the intersection of N(v) and D not equal to the intersection of N(u) and D with u not equal to v. The locating domination number of a graph G is the minimum cardinality of a locating dominating set in a graph G . In this study discussed the locating domin

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21

Ghanem, Manal, Hasan Al-Ezeh, and Ala’a Dabbour. "Locating Chromatic Number of Powers of Paths and Cycles." Symmetry 11, no. 3 (2019): 389. http://dx.doi.org/10.3390/sym11030389.

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Let c be a proper k-coloring of a graph G. Let π = { R 1 , R 2 , … , R k } be the partition of V ( G ) induced by c, where R i is the partition class receiving color i. The color code c π ( v ) of a vertex v of G is the ordered k-tuple ( d ( v , R 1 ) , d ( v , R 2 ) , … , d ( v , R k ) ) , where d ( v , R i ) is the minimum distance from v to each other vertex u ∈ R i for 1 ≤ i ≤ k . If all vertices of G have distinct color codes, then c is called a locating k-coloring of G. The locating-chromatic number of G, denoted by χ L ( G ) , is the smallest k such that G admits a locating coloring wit

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22

Raza, Hassan, Naveed Iqbal, Hamda Khan, and Thongchai Botmart. "Computing locating-total domination number in some rotationally symmetric graphs." Science Progress 104, no. 4 (2021): 003685042110534. http://dx.doi.org/10.1177/00368504211053417.

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Let [Formula: see text] be a connected graph. A locating-total dominating set in a graph G is a total dominating set S of a G, for every pair of vertices [Formula: see text], such that [Formula: see text]. The minimum cardinality of a locating-total dominating set is called locating-total domination number and represented as [Formula: see text]. In this paper, locating-total domination number is determined for some cycle-related graphs. Furthermore, some well-known graphs of convex polytopes from the literature are also considered for the locating-total domination number.

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Asmiati, A., Maharani Damayanti, and Lyra Yulianti. "On the Locating Chromatic Number of Barbell Shadow Path Graph." Indonesian Journal of Combinatorics 5, no. 2 (2021): 82. http://dx.doi.org/10.19184/ijc.2021.5.2.4.

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The locating-chromatic number was introduced by Chartrand in 2002. The locating chromatic number of a graph is a combined concept between the coloring and partition dimension of a graph. The locating chromatic number of a graph is defined as the cardinality of the minimum color classes of the graph. In this paper, we discuss about the locating-chromatic number of shadow path graph and barbell graph containing shadow graph.

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24

Zikra, Fakhri, DES WELYYANTI, and LYRA YULIANTI. "The Locating-chromatic Number of Disjoint Union of Fan Graphs." Jurnal Matematika UNAND 11, no. 3 (2022): 159. http://dx.doi.org/10.25077/jmua.11.3.159-170.2022.

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Let G = (V,E) is a connected graph and c is a k-coloring of G. The color class of G is the set of colored vertexs i, denoted by Ci for 1 <= i <= k. Let phi is a ordered partition from V (G) to independent color classes that is C1;C2; ...;Ck, with vertexs of Ci given color by i, 1 <= i <= k. Distance of a vertex v in V to Ci denoted by d(v,Ci) is min {d(v, x)|x in Ci}. The color codes of a vertex v in V is the ordered k-vector c(Phi|v) = (d(v,C1), d(v,C2), ..., d(v,Ck)) where d(v,Ci) = min {d(v, x | x in Ci)} for 1 <= i <= k. If distinct vertices have distinct color codes, the

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Bustan, Ariestha W., A. N. M. Salman, Pritta E. Putri, and Zata Y. Awanis. "On the Locating Rainbow Connection Number of Trees and Regular Bipartite Graphs." Emerging Science Journal 7, no. 4 (2023): 1260–73. http://dx.doi.org/10.28991/esj-2023-07-04-016.

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Locating the rainbow connection number of graphs is a new mathematical concept that combines the concepts of the rainbow vertex coloring and the partition dimension. In this research, we determine the lower and upper bounds of the locating rainbow connection number of a graph and provide the characterization of graphs with the locating rainbow connection number equal to its upper and lower bounds to restrict the upper and lower bounds of the locating rainbow connection number of a graph. We also found the locating rainbow connection number of trees and regular bipartite graphs. The method used

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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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Savic, Aleksandar, Zoran Maksimovic, and Milena Bogdanovic. "The open-locating-dominating number of some convex polytopes." Filomat 32, no. 2 (2018): 635–42. http://dx.doi.org/10.2298/fil1802635s.

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In this paper we will investigate the problem of finding the open-locating-dominating number for some classes of planar graphs - convex polytopes. We considered Dn, Tn, Bn, Cn, En and Rn classes of convex polytopes known from the literature. The exact values of open-locating-dominating number for Dn and Rn polytopes are presented, along with the upper bounds for Tn, Bn, Cn, and En polytopes.

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Anti, A., D. Welyyanti, and M. Azhari. "On Locating Chromatic Number of H = Pm ∪ Wn." Journal of Physics: Conference Series 1742 (January 2021): 012024. http://dx.doi.org/10.1088/1742-6596/1742/1/012024.

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29

Pribadi, Aswan Anggun, and Suhadi Wido Saputro. "On locating-dominating number of comb product graphs." Indonesian Journal of Combinatorics 4, no. 1 (2020): 27. http://dx.doi.org/10.19184/ijc.2020.4.1.4.

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<div class="page" title="Page 1"><div class="layoutArea"><div class="column"><div class="page" title="Page 1"><div class="layoutArea"><div class="column"><p><span>We consider a set </span><span><em>D</em> </span><span>⊆ </span><em>V</em><span>(</span><em>G</em><span>) </span><span>which dominate </span><span><em>G</em> </span><span>and for every two distinct vertices </span><span><em>x</em>, &

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Baskoro, Edy Tri, and Asmiati Asmiati. "Characterizing all trees with locating-chromatic number 3." Electronic Journal of Graph Theory and Applications 1, no. 2 (2013): 109–17. http://dx.doi.org/10.5614/ejgta.2013.1.2.4.

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Dafik, Ika Hesti Agustin, Ermita Rizki Albirri, Ridho Alfarisi, and R. M. Prihandini. "Locating domination number of m-shadowing of graphs." Journal of Physics: Conference Series 1008 (April 2018): 012041. http://dx.doi.org/10.1088/1742-6596/1008/1/012041.

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Nur Santi, Risan, Ika Hesti Agustin, Dafik, and Ridho Alfarisi. "On the locating domination number of corona product." Journal of Physics: Conference Series 1008 (April 2018): 012053. http://dx.doi.org/10.1088/1742-6596/1008/1/012053.

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Irawan, Agus, and Asmiati. "The locating-chromatic number of subdivision firecracker graphs." International Mathematical Forum 13, no. 10 (2018): 485–92. http://dx.doi.org/10.12988/imf.2018.8844.

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Retno Wardani, Dwi Agustin, Dafik, Ika Hesti Agustin, and Elsa Yuli Kurniawati. "On locating independent domination number of amalgamation graphs." Journal of Physics: Conference Series 943 (December 2017): 012027. http://dx.doi.org/10.1088/1742-6596/943/1/012027.

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Behtoei, Ali, and Behnaz Omoomi. "On the locating chromatic number of Kneser graphs." Discrete Applied Mathematics 159, no. 18 (2011): 2214–21. http://dx.doi.org/10.1016/j.dam.2011.07.015.

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Prakash, V. "An efficientg-centroid location algorithm for cographs." International Journal of Mathematics and Mathematical Sciences 2005, no. 9 (2005): 1405–13. http://dx.doi.org/10.1155/ijmms.2005.1405.

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In 1998, Pandu Rangan et al. Proved that locating theg-centroid for an arbitrary graph is𝒩𝒫-hard by reducing the problem of finding the maximum clique size of a graph to theg-centroid location problem. They have also given an efficient polynomial time algorithm for locating theg-centroid for maximal outerplanar graphs, Ptolemaic graphs, and split graphs. In this paper, we present anO(nm)time algorithm for locating theg-centroid for cographs, wherenis the number of vertices andmis the number of edges of the graph.

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Irawan, Agus, and Ana Istiani. "The Locating Chromatic Number for the New Operation on Generalized Petersen Graphs N_P(m,1)." Sainmatika: Jurnal Ilmiah Matematika dan Ilmu Pengetahuan Alam 21, no. 1 (2024): 89–96. http://dx.doi.org/10.31851/sainmatika.v21i1.14864.

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The locating chromatic number is a graph invariant that quantifies the minimum number of colors required for proper vertex coloring, ensuring that any two vertices with the same color have distinct sets of neighbors. This study introduces a new operation on generalized Petersen graphs denoted by N_(P(m,1)), exploring its impact on locating chromatic numbers. Through systematic analysis, we aim to determine the specific conditions under which this operation influences the locating chromatic number and provide insights into the underlying graph-theoretical properties. The method for computing th

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Bustan, A. W., A. N. M. Salman, and P. E. Putri. "On the locating rainbow connection number of amalgamation of complete graphs." Journal of Physics: Conference Series 2543, no. 1 (2023): 012004. http://dx.doi.org/10.1088/1742-6596/2543/1/012004.

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Abstract Locating rainbow connection number determines the minimum number of colors connecting any two vertices of a graph with a rainbow vertex path and also verifies that the given colors produce a different rainbow code for each vertex. Locating rainbow connection number of graphs is a new mathematical concept, especially in graph theory, which combines the concepts of the rainbow vertex coloring and the partition dimension. In this paper, we determine the locating rainbow connection number of amalgamation of complete graphs.

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Welyyanti, Des, Latifa Azhar Abel, and Lyra Yulianti. "THE LOCATING CHROMATIC NUMBER OF CHAIN(A,4,n) GRAPH." BAREKENG: Jurnal Ilmu Matematika dan Terapan 19, no. 1 (2025): 353–60. https://doi.org/10.30598/barekengvol19iss1pp353-360.

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Let be a connected graph with a vertex coloringsuch that two adjacent vertices have different colors. We denote an ordered partition where is a color class with color-, consisting of vertices given color , for . The color code of a vertex in is a -vector: . where is the distance between a vertex in and for . If every two vertices and in have different color codes, , then is called the locating -coloring of . The minimum number of colors k needed in this coloring is defined as the locating chromatic number, denoted by . This paper determines the locating chromatic number of chain graph and the

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Asmiati, I. Ketut Sadha Gunce Yana, and Lyra Yulianti. "On the Locating Chromatic Number of Certain Barbell Graphs." International Journal of Mathematics and Mathematical Sciences 2018 (August 5, 2018): 1–5. http://dx.doi.org/10.1155/2018/5327504.

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The locating chromatic number of a graph G is defined as the cardinality of a minimum resolving partition of the vertex set V(G) such that all vertices have distinct coordinates with respect to this partition and every two adjacent vertices in G are not contained in the same partition class. In this case, the coordinate of a vertex v in G is expressed in terms of the distances of v to all partition classes. This concept is a special case of the graph partition dimension notion. In this paper we investigate the locating chromatic number for two families of barbell graphs.

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Zulkarnain, Debi, Lyra Yulianti, Des Welyyanti, Kiki Khaira Mardimar, and Muhammad Rafif Fajri. "ON THE LOCATING CHROMATIC NUMBER OF DISJOINT UNION OF BUCKMINSTERFULLERENE GRAPHS." BAREKENG: Jurnal Ilmu Matematika dan Terapan 18, no. 2 (2024): 0915–22. http://dx.doi.org/10.30598/barekengvol18iss2pp0915-0922.

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Let be a connected non-trivial graph. Let c be a proper vertex-coloring using k colors, namely . Let be a partition of induced by , where is the color class that receives the color . The color code, denoted by , is defined as , where for , and is the distance between two vertices and in G. If all vertices in have different color codes, then is called as the locating-chromatic -coloring of . The locating-chromatic number of , denoted by , is the minimum such that has a locating coloring. Let be the Buckminsterfullerene graph on vertices. Buckminsterfullerene graph is a 3-connected planar graph

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Sumathi, P., and G. Alarmelumangai. "Locating Equitable Domination and Independence Subdivision Numbers of Graphs." Bulletin of Mathematical Sciences and Applications 9 (August 2014): 27–32. http://dx.doi.org/10.18052/www.scipress.com/bmsa.9.27.

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Let G = (V,E) be a simple, undirected, finite nontrivial graph. A non empty set DV of vertices in a graph G is a dominating set if every vertex in V-D is adjacent to some vertex in D. The domination number (G) is the minimum cardinality of a dominating set of G. A dominating set D is a locating equitable dominating set of G if for any two vertices u,wєV-D, N(u)∩D ≠ N(w)∩D, |N(u)∩D| ≠ |N(w)∩D|. The locating equitable domination number of G is the minimum cardinality of a locating equitable dominating set of G. The locating equitable domination subdivision number of G is the minimum number of ed

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Shaju, Varughese. "Facility Location in Logistic Network Design Using Soft Computing Opimization Models." International Journal of Computer Science & Information Technology (IJCSIT) 9, no. 5 (2017): 51–65. https://doi.org/10.5281/zenodo.1212368.

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Discovery of the optimal best possibility of location for facilities is the central problem associated in logistics management. The optimal places for the distribution centres (DCs) can be based on the selected attributes that are crucial to locate the best possible locations to increase the speed of the facility service and thus reduce the overall transport cost and time and to provide best service. The major task is to identifying and locating the required number of DCs and its optimum locations are considered as the important goals for the design of any logistics network. The number of DCs

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Abel, Latifa Azhar, Des Welyyanti, Lyra Yulianti, and Dony Permana. "The Locating Chromatic Number of the Cyclic Chain Graph." Science and Technology Indonesia 10, no. 3 (2025): 978–82. https://doi.org/10.26554/sti.2025.10.3.978-982.

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The locating chromatic number of graph G (χL(G)) combines the idea of the partition dimension and the chromatic number by considering the locations of the vertices of graph G. Let (Cni, m) be a cyclic chain graph, namely a group of blocks in the form of a cycle graph Cn1(1), Cn2(2), ···, Cni(i). The ni is the number of vertices on the i-th cycle, and m is the number of cycles, for ni ≥ 3, 1 ≤ i ≤ m, and m ≥ 2, and the vertex vi,⌈ni/2⌉+1 in Cni(i) is identified with the vertex vi,⌈ni/2⌉+1 in Cni+1(i+1). In this research, we determine χL(Cni, m) for ni ≥ 3, 1 ≤ i ≤ m, and m ≥ 2.

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Abel, Latifa Azhar, Des Welyyanti, Lyra Yulianti, and Dony Permana. "The Locating Chromatic Number of the Cyclic Chain Graph." Science and Technology Indonesia 10, no. 3 (2025): 958–62. https://doi.org/10.26554/sti.2025.10.3.958-962.

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The locating chromatic number of graph G (χL(G)) combines the idea of the partition dimension and the chromatic number by considering the locations of the vertices of graph G. Let (Cni, m) be a cyclic chain graph, namely a group of blocks in the form of a cycle graph Cn1(1), Cn2(2), ···, Cni(i). The ni is the number of vertices on the i-th cycle, and m is the number of cycles, for ni ≥ 3, 1 ≤ i ≤ m, and m ≥ 2, and the vertex vi,⌈ni/2⌉+1 in Cni(i) is identified with the vertex vi,⌈ni/2⌉+1 in Cni+1(i+1). In this research, we determine χL(Cni, m) for ni ≥ 3, 1 ≤ i ≤ m, and m ≥ 2.

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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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Jafari Rad, Nader, and Hadi Rahbani. "Bounds on the locating-domination number and differentiating-total domination number in trees." Discussiones Mathematicae Graph Theory 38, no. 2 (2018): 455. http://dx.doi.org/10.7151/dmgt.2012.

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Raza, Hassan. "Computing Open Locating-Dominating Number of Some Rotationally-Symmetric Graphs." Mathematics 9, no. 12 (2021): 1415. http://dx.doi.org/10.3390/math9121415.

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Location detection is studied for many scenarios, such as pointing out the flaws in multiprocessors, invaders in buildings and facilities, and utilizing wireless sensor networks for monitoring environmental processes. The system or structure can be illustrated as a graph in each of these applications. Sensors strategically placed at a subset of vertices can determine and identify irregularities within the network. The open locating-dominating set S of a graph G=(V,E) is the set of vertices that dominates G, and for any i,j∈ V(G) N(i)∩S≠N(j)∩S is satisfied. The set S is called the OLD-set of G.

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Hartiansyah, Fiqih, and Darmaji Darmaji. "Bilangan Kromatik Lokasi pada Graf Hasil Amalgamasi Sisi dari Graf Bintang dan Graf Lengkap." Zeta - Math Journal 8, no. 2 (2023): 66–70. http://dx.doi.org/10.31102/zeta.2023.8.2.66-70.

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The locating coloring of graph extends the vertex coloring dan partition dimension of graph. The minimum number of locating coloring of graph G is called the locating chromatic number of graph G. In this paper will discuss the locating chromatic number of edge amalgamation graph of star graph with order m+1 and complete graph with order n. The method used to obtain the locating chromatic number of graph is to determine the upper dan lower bound. The results obtained are that the locating chromatic number of edge amalgamation graph of star graph with order m+1 and complete graph with order n is

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Prawinasti, K., M. Ansori, Asmiati, Notiragayu, and AR G N Rofi. "The Locating Chromatic Number for Split Graph of Cycle." Journal of Physics: Conference Series 1751 (January 2021): 012009. http://dx.doi.org/10.1088/1742-6596/1751/1/012009.

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