Further new results on strong resolving partitions for graphs [PDF]
Open Mathematics, 2020 A set W of vertices of a connected graph G strongly resolves two different vertices x, y ∉ W if either d G(x, W) = d G(x, y) + d G(y, W) or d G(y, W) = d G(y, x) + d
Dorota Kuziak, Ismael G Yero
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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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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 +2 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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Computation of Resolvability Parameters for Benzenoid Hammer Graph
Journal of Mathematics, 2022 A representation of each vertex of a network into distance-based arbitrary tuple form, adding the condition of uniqueness of each vertex with reference to some settled vertices. Such settled vertices form a set known as resolving set.
Ali Ahmad, Al-Nashri Al-Hossain Ahmad
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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
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Simulating the Greenland ice sheet under present-day and palaeo constraints including a new discharge parameterization [PDF]
The Cryosphere, 2015 In this paper, we propose a new sub-grid scale parameterization for the ice discharge into the ocean through outlet glaciers and inspect the role of different observational and palaeo constraints for the choice of an optimal set of model parameters. This
R. Calov +3 more
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Cardinality bounds on subsets in the partition resolving set for complex convex polytope-like graph
AIMS Mathematics<abstract><p>Let $ G = (V, E) $ be a simple, connected graph with vertex set $ V(G) $ and $ E(G) $ edge set of $ G $. For two vertices $ a $ and $ b $ in a graph $ G $, the distance $ d(a, b) $ from $ a $ to $ b $ is the length of shortest path $ a-b $ path in $ G $. A $ k $-ordered partition of vertices of $ G $ is represented as $ {R}{p} =
Ali N A Koam +2 more
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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 Tri-Hexagonal α-Boron Nanotube
IEEE Access, 2021 The production of low-cost, small in size, and high in efficiency objects is the topic of research in almost all scientific fields, especially of engineering. In this scenario, nanotechnology becomes of great importance. To achieve these tasks, one needs
Ayesha Shabbir, Muhammad Azeem
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