Results 11 to 20 of about 6,232 (95)
Sharp bounds for partition dimension of generalized Möbius ladders
Open Mathematics, 2018 The concept of minimal resolving partition and resolving set plays a pivotal role in diverse areas such as robot navigation, networking, optimization, mastermind games and coin weighing.
Hussain Zafar +4 more
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Dimensi Metrik Graf Kr+mKsr, m, r, s, En
Cauchy: Jurnal Matematika Murni dan Aplikasi, 2011 The concept of minimum resolving set has proved to be useful and or related to a variety of fields such as Chemistry, Robotic Navigation, and Combinatorial Search and Optimization. So that, this thesis explains the metric dimension of graph Kr + mKsr, m,
Hindayani Hindayani
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Conditional resolvability in graphs: a survey
International Journal of Mathematics and Mathematical Sciences, 2004 For an ordered set W={w1,w2,…,wk} of vertices and a vertex v in a connected graph G, the code of v with respect to W is the k-vector cW(v)=(d(v,w1),d(v,w2),…,d(v,wk)), where d(x,y) represents the distance between the vertices x and y.
Varaporn Saenpholphat, Ping Zhang
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Partition Dimension of Generalized Hexagonal Cellular Networks and Its Application
IEEE AccessThe notion of partition dimension was initially introduced in the field of graph theory, primarily to examine distances between vertices. The local partition dimension extends this idea by incorporating specific conditions into how vertices are ...
Rabnawaz Bhatti +3 more
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Trees with Certain Locating-chromatic Number
Journal of Mathematical and Fundamental Sciences, 2016 The locating-chromatic number of a graph G can be 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 ...
Dian Kastika Syofyan +2 more
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On the Locating Chromatic Number of Certain Barbell Graphs
International Journal of Mathematics and Mathematical Sciences, 2018 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 ...
Asmiati +2 more
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Cardinality bounds on subsets in the partition resolving set for complex convex polytope-like graph
AIMS Mathematics<abstract><p>Let $ G = (V, E) $ be a simple, connected graph with vertex set $ V(G) $ and $ E(G) $ edge set of $ G $. For two vertices $ a $ and $ b $ in a graph $ G $, the distance $ d(a, b) $ from $ a $ to $ b $ is the length of shortest path $ a-b $ path in $ G $. A $ k $-ordered partition of vertices of $ G $ is represented as $ {R}{p} =
Ali N. A. Koam +3 more
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THE PARTITION DIMENSION OF CYCLE BOOKS GRAPH B_(m,n) WITH A COMMON PATH P_2
BarekengSuppose is a connected graph with elements of a set of vertices denoted by and a subset of . The distance between and is the shortest distance to every vertex in . Let be a partition of , where each subset belongs to .
Jaya Santoso, Darmaji Darmaji
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The Mixed Partition Dimension: A New Resolvability Parameter in Graph Theory
IEEE AccessIn this article, we introduce a novel graph-theoretical parameter called the mixed partition dimension and apply it to the path graph and the hexagonal network.
Siti Norziahidayu Amzee Zamri +4 more
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Exchange Property in Double Edge Resolving Partition Sets and Its Use in City Development
Spectrum of Decision Making and ApplicationsThe exchange property in double-edge resolving partition sets is examined in this article, along with some real-world applications to city buildings. In graph theory, double-edge resolving sets are essential because they provide information on optimizing transportation and urban infrastructure. When utility units are switched out, the exchange property
Sikander Ali, Muhammad Kamran Jamil
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