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Double edge resolving set and exchange property for nanosheet structure [PDF]

Heliyon
The exploration of edge metric dimension and its applications has been an ongoing discussion, particularly in the context of nanosheet graphs formed from the octagonal grid. Edge metric dimension is a concept that involves uniquely identifying the entire
Ali N.A. Koam, Ali Ahmad, Sikander Ali, Muhammad Kamran Jamil, Muhammad Azeem   +4 more
doaj   +5 more sources

Optimal Fault-Tolerant Resolving Set of Power Paths

Mathematics, 2023
In a simple connected undirected graph G, an ordered set R of vertices is called a resolving set if for every pair of distinct vertices u and v, there is a vertex w∈R such that d(u,w)≠d(v,w).
Laxman Saha, Rupen Lama, Bapan Das, Avishek Adhikari, Kinkar Chandra Das   +4 more
doaj   +4 more sources

On the Characterization of a Minimal Resolving Set for Power of Paths

Mathematics, 2022
For a simple connected graph G=(V,E), an ordered set W⊆V, is called a resolving set of G if for every pair of two distinct vertices u and v, there is an element w in W such that d(u,w)≠d(v,w).
Laxman Saha, Mithun Basak, Kalishankar Tiwary, Kinkar Chandra Das, Yilun Shang   +4 more
doaj   +4 more sources

Independent resolving sets in graphs [PDF]

AKCE International Journal of Graphs and Combinatorics, 2021
Let be a connected graph. Let be a subset of V with an order imposed on W. The k-vector is called the resolving vector of v with respect to W. The set W is called a resolving set if for any two distinct vertices In this paper we investigate the existence
B. Suganya, S. Arumugam
doaj   +2 more sources

A Study of Independency on Fuzzy Resolving Sets of Labelling Graphs

Mathematics, 2023
Considering a fuzzy graph G is simple and can be connected and considered as a subset H=u1,σu1,u2,σu2,…uk,σuk, |H|≥2; then, every two pairs of elements of σ−H have a unique depiction with the relation of H, and H can be termed as a fuzzy resolving set ...
Ramachandramoorthi Shanmugapriya, Perichetla Kandaswamy Hemalatha, Lenka Cepova, Jiri Struz   +3 more
doaj   +2 more sources

Optimal Multi-Level Fault-Tolerant Resolving Sets of Circulant Graph C(n : 1, 2)

Mathematics, 2023
Let G=(V(G),E(G)) be a simple connected unweighted graph. A set R⊂V(G) is called a fault-tolerant resolving set with the tolerance level k if the cardinality of the set Sx,y={w∈R:d(w,x)≠d(w,y)} is at least k for every pair of distinct vertices x,y of G ...
Laxman Saha, Bapan Das, Kalishankar Tiwary, Kinkar Chandra Das, Yilun Shang   +4 more
doaj   +2 more sources

Properties of Fuzzy Resolving Set

Turkish Journal of Computer and Mathematics Education (TURCOMAT), 2021
Asbract: In a fuzzy graph G(v, σ, μ), for a subset H of σ, the representation of σ − H with respect to H in terms of strength of connectedness of vertices are distinct then H is called the fuzzy resolving set of G.
D. Mary Jiny
semanticscholar   +3 more sources

Topological insights into breast cancer drugs: a QSPR approach using resolving topological indices [PDF]

Frontiers in Chemistry
IntroductionBreast cancer, one of the most prevalent malignancies in women begins in the milk ducts or lobules and is divided into invasive and non-invasive variants.
E. Pandeeswari, J. Ravi Sankar
doaj   +2 more sources

Resolving set and exchange property in nanotube

AIMS Mathematics, 2023
Give us a linked graph, $ G = (V, E). $ A vertex $ w\in V $ distinguishes between two components (vertices and edges) $ x, y\in E\cup V $ if $ d_G(w, x)\neq d_G (w, y). $ Let $ W_{1} $ and $ W_{2} $ be two resolving sets and $ W_{1} $ $ \neq $ $ W_{2} $.
Ali N. A. Koam, Sikander Ali, A. Ahmad, Muhammad Azeem, M. Jamil   +4 more
semanticscholar   +3 more sources

Resolving Sets in Temporal Graphs

International Workshop on Combinatorial Algorithms
A \emph{resolving set} $R$ in a graph $G$ is a set of vertices such that every vertex of $G$ is uniquely identified by its distances to the vertices of $R$.
Jan Bok, Antoine Dailly, Tuomo Lehtilä
semanticscholar   +4 more sources