Results 11 to 20 of about 27,973 (272)
The edge partition dimension of graphs [PDF]
Discrete Mathematics Letters, 2023 Theedgemetric dimension wasintroduced in 2018 and since then, it has been extensively studied. In this paper, we present a different way to obtain resolving structures in graphs in order to gain more insight into the study of edge resolving sets ...
Dorota Kuziak +3 more
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All graphs of order n ≥ 11 and diameter 2 with partition dimension n − 3 [PDF]
Heliyon, 2020 All graphs of order n with partition dimension 2, n−2, n−1, or n have been characterized. However, finding all graphs on n vertices with partition dimension other than these above numbers is still open.
Edy Tri Baskoro
exaly +4 more sources
Bounds for partition dimension of M-wheels
Open Physics, 2019 Resolving partition and partition dimension have multipurpose applications in computer, networking, optimization, mastermind games and modelling of chemical substances.
Zafar Hussain +2 more
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The partition dimension of a subdivision of a homogeneous firecracker [PDF]
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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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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Computing the partition dimension of certain families of Toeplitz graph [PDF]
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 partition dimension of the vertex amalgamation of some cycles [PDF]
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 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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Local Partition Dimension of Grid Graph and Its Application to the Coordinates of Potential Disaster Areas in Jember Regency [PDF]
JTAM (Jurnal Teori dan Aplikasi Matematika), 2023 Partition dimension was introduced as a part of interesting topic in graph theory. It was focus to observe about distance. The local partition dimension is an expansion of the partition dimension by adding certain conditions to the representation of the ...
Ilham Saifudin +2 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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