Results 11 to 20 of about 6,806 (225)
On The Partition Dimension of Disconnected Graphs
Journal of Mathematical and Fundamental Sciences, 2017 For a graph G=(V,E), a partition Ω=\{O_1,O_2,…,O_k \} of the vertex set V is called a resolving partition if every pair of vertices u,v∈V(G) have distinct representations under Ω.
Debi Oktia Haryeni +2 more
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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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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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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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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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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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On the Constant Partition Dimension of Some Generalized Families of Toeplitz Graph
Journal of MathematicsThe use of graph theory is prevalent in the field of network design, whereby it finds utility in several domains such as the development of integrated circuits, communication networks, and transportation systems. The comprehension of partition dimensions
Ali N. A. Koam +4 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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Bounds on partition dimension of Peterson graphs
, 2021 The distance of a connected, simple graph P is denoted by d(eta(1), eta(2)), which is the length of a shortest path between the vertices eta(1), eta(2) is an element of V(P), where V(P) is the vertex set of P. The l- ordered partition of V(P) is theta = (
Azeem, Muhammasd +9 more
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On bounded partition dimension of different families of convex polytopes with pendant edges
, 2021 Let ψ=(V,E) be a simple connected graph. The distance between ρ1,ρ2∈V(ψ) is the length of a shortest path between ρ1 and ρ2. Let Γ={Γ1,Γ2,…,Γj} be an ordered partition of the vertices of ψ . Let ρ1∈V(ψ) , and r(ρ1|Γ)={d(ρ1,Γ1),d(ρ1,Γ2),…,d(ρ1,
Khali, Adnan +2 more
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