Results 21 to 30 of about 718 (221)
On Resolvability- and Domination-Related Parameters of Complete Multipartite Graphs
Mathematics, 2022 Graphs of order n with fault-tolerant metric dimension n have recently been characterized.This paper points out an error in the proof of this characterization. We show that the complete multipartite graphs also have the fault-tolerant metric dimension n,
Sakander Hayat, Asad Khan, Yubin Zhong
doaj +1 more source
The Fault-Tolerant Metric Dimension of Cographs [PDF]
, 2019 arXiv admin note: text overlap with arXiv:1806 ...
Duygu Vietz, Egon Wanke
openaire +3 more sources
The Application of Fault-Tolerant Partition Resolvability in Cycle-Related Graphs
Applied Sciences, 2022 The concept of metric-related parameters permeates all of graph theory and plays an important role in diverse networks, such as social networks, computer networks, biological networks and neural networks.
Kamran Azhar +4 more
doaj +1 more source
Bounds for metric dimension and defensive $k$-alliance of graphs under deleted lexicographic product [PDF]
Transactions on Combinatorics, 2020 Metric dimension and defensive $k$-alliance number are two distance-based graph invariants which have applications in robot navigation, quantitative analysis of secondary RNA structures, national defense and fault-tolerant computing.
Kinkar Chandra Das, Mostafa Tavakoli
doaj +1 more source
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 +4 more
doaj +1 more source
Fault-Tolerant Resolvability in Some Classes of Subdivision Graphs
Journal of Mathematics, 2022 The concept of resolving sets (RSs) and metric dimension (MD) invariants have a wide range of applications in robot navigation, computer networks, and chemical structure. RS has been used as a sensor in an indoor positioning system to find an interrupter.
Muhammad Faheem +4 more
doaj +1 more source
Fault-Tolerant Resolvability and Extremal Structures of Graphs
Mathematics, 2019 In this paper, we consider fault-tolerant resolving sets in graphs. We characterize n-vertex graphs with fault-tolerant metric dimension n, n − 1 , and 2, which are the lower and upper extremal cases.
Hassan Raza +3 more
doaj +1 more source
Computation of Edge Resolvability of Benzenoid Tripod Structure
Journal of Mathematics, 2021 In chemistry, graphs are commonly used to show the structure of chemical compounds, with nodes and edges representing the atom and bond types, respectively.
Ali Ahmad +4 more
doaj +1 more source
Fault-Tolerant Partition Resolvability of Cyclic Networks
Journal of Mathematics, 2021 Graph invariants provide an amazing tool to analyze the abstract structures of networks. The interaction and interconnection between devices, sensors, and service providers have opened the door for an eruption of mobile over the web applications ...
Kamran Azhar +3 more
doaj +1 more source
Fault-Tolerant Metric Dimension of Cube of Paths
Journal of Physics: Conference Series, 2021 Abstract For a simple connected graph G = (V (G), E(G)), a set R ⊆ V (G) is said to be a resolving set of G if every pair of vertices of G are resolved by some vertices in R i.e., every pair of vertices of G are identified uniquely by some vertex elements in F.
openaire +1 more source