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The connected partition dimension of truncated wheels [PDF]
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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Partition dimension of projective planes [PDF]
European Journal of Combinatorics, 2017 We determine the partition dimension of the incidence graph G(Πq) of the projective plane Πq up to a constant factor 2 as (2+o(1))log2q≤pd(G(Πq))≤(4+o(1))log2q.
Blázsik, ZL +5 more
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Partition dimension of trees - palm approach
Electronic Journal of Graph Theory and ApplicationsThe partition dimension of a graph is the minimum number of vertex partitions such that every vertex has different distances to the ordered partitions. Many resolving partitions for trees have all vertices not in an end-path in the same partition.
Yusuf Hafidh, Edy Tri Baskoro
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Connected partition dimensions of graphs
Discussiones Mathematicae Graph Theory, 2002 For a vertex v of a connected graph G and a subset S of V(G), the distance between v and S is d(v,S) = min{d(v,x)|x ∈ S}. For an ordered k-partition Π = {S₁,S₂,...,Sₖ} of V(G), the representation of v with respect to Π is the k-vector r(v|Π) = (d(v,S₁ ...
Saenpholphat, Varaporn, Zhang, Ping
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Partition Resolvability of Nanosheet and Nanotube Derived from Octagonal Grid
Journal of MathematicsChemical graph theory, a branch of computational and applied mathematics, covers a very wide range of topics. As a result, the world of applied sciences heavily relies on graph theory.
Ali Al Khabyah +2 more
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Discrepancies between metric dimension and partition dimension of a connected graph
Discrete Mathematics, 2007 Let (Z2,E4) and (Z2,E8) be graphs where the set of vertices is the set of points of the integer lattice and the set of edges consists of all pairs of vertices whose city block and chessboard distances, respectively, are 1.In this paper it is shown that ...
Ioan Tomescu, Tomescu, Ioan
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Partitioning point sets in arbitrary dimension
Theoretical Computer Science, 1987 We introduce a new type of partition called a parallel planes partition. We prove there exists a parallel planes partition of any set of n points in arbitrary dimension.
Cole, Richard
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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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Brick partition problems in three dimensions [PDF]
Discrete Mathematics, 2021 A $d$-dimensional brick is a set $I_1\times \cdots \times I_d$ where each $I_i$ is an interval. Given a brick $B$, a brick partition of $B$ is a partition of $B$ into bricks. A brick partition $\mathcal{P}_d$ of a $d$-dimensional brick is $k$-piercing if every axis-parallel line intersects at least $k$ bricks in $\mathcal{P}_d$. Bucic et al. explicitly
Ilkyoo Choi, Minseong Kim, Kiwon Seo
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Fault-Tolerant Partition Resolvability in Mesh Related Networks and Applications
IEEE Access, 2022 Fault-tolerance of a system measures its working capability in the presence of faulty components in the system. The fault-tolerant partition dimension of a network computes the least number of subcomponents of network required to distinctively identify ...
Kamran Azhar +4 more
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