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Fault-tolerant partition resolvability of cycle with chord. [PDF]
PLoS ONEIn the realm of connected networks, distance-based parameters, particularly the partition dimension of graphs, have extensive applications across various fields, including chemistry and computer science.
Kamran Azhar +3 more
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Computing the partition dimension of certain families of Toeplitz graph
Frontiers in Computational Neuroscience, 2022 Let G = (V(G), E(G)) be a graph with no loops, numerous edges, and only one component, which is made up of the vertex set V(G) and the edge set E(G). The distance d(u, v) between two vertices u, v that belong to the vertex set of H is the shortest path ...
Ricai Luo +5 more
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The connected partition dimension of truncated wheels
AKCE International Journal of Graphs and Combinatorics, 2021 Let G be a connected graph. For a vertex v of G and a subset S of V(G), the distance between v and S is d(v, S) = min Given an ordered k-partition = of V(G), the representation of v with respect to is the k-vector If for each pair of distinct vertices ...
Lyndon L. Lazaro, Jose B. Rosario
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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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Partition Dimension of Generalized Petersen Graph
Complexity, 2021 Let G=VG,EG be the connected graph. For any vertex i∈VG and a subset B⊆VG, the distance between i and B is di;B=mindi,j|j∈B. The ordered k-partition of VG is Π=B1,B2,…,Bk. The representation of vertex i with respect to Π is the k-vector, that is, ri|Π=di,
Hassan Raza +3 more
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On Partition Dimension of Generalized Convex Polytopes
Journal of Mathematics, 2023 Let G be a graph having no loop or multiple edges, k−order vertex partition for G is represented by γ=γ1,γ2,…,γk. The vector rϕγ=dϕ,γ1,dϕ,γ2,dϕ,γ3⋯,dϕ,γk is the representation of vertex ϕ with respect to γ.
Syed Waqas Shah +5 more
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The partition dimension of a subdivision of a homogeneous firecracker
Electronic Journal of Graph Theory and Applications, 2020 Finding the partition dimension of a graph is one of the interesting (and uncompletely solved) problems of graph theory. For instance, the values of the partition dimensions for most kind of trees are still unknown. Although for several classes of trees
Amrullah Amrullah
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The partition dimension of the vertex amalgamation of some cycles
Heliyon, 2022 Let G=(V(G),E(G)) be a connected, finite, simple, and undirected graph. The distance between two vertices u,w∈V(G), denoted by d(u,w), is the shortest length of (u,w)-path in G.
Hasmawati +4 more
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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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