Results 1 to 10 of about 27,973 (272)
On the partition dimension of trees
Discrete Applied Mathematics, 2014 10.1016/j.dam.2013.09.026Given an ordered partition ?={P1,P2,., Pt} of the vertex set V of a connected graph G=(V,E), the partition representation of a vertex v?V with respect to the partition ? is the vector r(v|?)=(d(v,P1),d(v,P2),.,d(v,Pt)), where d(v,
Juan A Rodríguez-Velázquez +2 more
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Partition Dimension of Some Classes of Trees
Procedia Computer Science, 2015 Chartrand, E. Salehi and P. Zhang (1998) studied the concept of graph partition dimension as a new approach to settle the problem of finding the metric dimension of a graph. Now, the partition dimensions of many classes of trees have been known. However,
Edy Tri Baskoro
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The Partition Dimension of Some Families of Trees
Procedia Computer Science, 2015 In 1998, Chartrand, E. Salehi and P. Zhang introduced the concept of graph partition dimension. This is a variant of graph metric dimension concept introduced independently by Slater in 1975 and Harary & Melter in 1976.
Edy Tri Baskoro
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The Partition Dimension of a Subdivision of a Complete Graph
Procedia Computer Science, 2015 The concept of a graph partition dimension was introduced by Chartrand et al. (1998). Let Π = {L1, L2, L3, · · ·, Lk } be a k-partition of V(G). The representation r(v|Π) of a vertex v with respect to Π is the vector (d(v, L1), d(v, L2), · · ·, d(v, Lk)).
Amrullah +2 more
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On the Bounded Partition Dimension of Some Generalised Graph Structures
Journal of Mathematics, 2022 Consider λ to be a connected graph with a vertex set Vλ that may be partitioned into any partition set S. If each vertex in λ has a separate representation with regard to S and is an ordered k partition, then the set with S is a resolving partition of λ..
Wajdi Alghamdi, Muhammad Ahsan Asim
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Partition dimension of disjoint union of complete bipartite graphs
Desimal, 2021 For any (not necessary connected) graph $G(V,E)$ and $A\subseteq V(G)$, the distance of a vertex $x\in V(G)$ and $A$ is $d(x,A)=\min\{d(x,a): a\in A\}$. A subset of vertices $A$ resolves two vertices $x,y \in V(G)$ if $d(x,A)\neq d(y,A)$.
Debi Oktia Haryeni +2 more
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Fault-Tolerant Partition Resolvability of Cyclic Networks
Journal of Mathematics, 2021 Graph invariants provide an amazing tool to analyze the abstract structures of networks. The interaction and interconnection between devices, sensors, and service providers have opened the door for an eruption of mobile over the web applications ...
Kamran Azhar +3 more
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The partition dimension of strong product graphs and Cartesian product graphs [PDF]
Discrete Mathematics, 2014 10.1016/j.disc.2014.04.026LetG = (V,E) be a connected graph. The distance between two vertices u, v ? V, denoted by d(u, v), is the length of a shortest u, v-path in G. The distance between a vertex v ? V and a subset P ? V is defined as min{d(v, x) : x ?
Ismael G Yero +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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