Twin vertices in fault-tolerant metric sets and fault-tolerant metric dimension of multistage interconnection networks [PDF]
Applied Mathematics and Computation, 2022 A set of vertices $S\subseteq V(G)$ is a basis or resolving set of a graph $G$ if for each $x,y\in V(G)$ there is a vertex $u\in S$ such that $d(x,u)\neq d(y,u)$. A basis $S$ is a fault-tolerant basis if $S\setminus \{x\}$ is a basis for every $x \in S$.
Prabhu, S. +3 more
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Fault-tolerant metric dimension of zero-divisor graphs of commutative rings [PDF]
AKCE International Journal of Graphs and Combinatorics, 2021 Let R be a commutative ring with identity. The zero-divisor graph of R denoted by is an undirected graph where is the set of non-zero zero-divisors of R and there is an edge between the vertices z1 and z2 in if A set of vertices S resolves a graph G if ...
Sahil Sharma, Vijay Kumar Bhat
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Fault-Tolerant Metric Dimension in Carbon Networks
FoundationsIn this paper, we study the fault-tolerant metric dimension in graph theory, an important measure against failures in unique vertex identification. The metric dimension of a graph is the smallest number of vertices required to uniquely identify every ...
Kamran Azhar, Asim Nadeem, Yilun Shang
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Studies of Multilevel Networks via Fault-Tolerant Metric Dimensions
IEEE Access, 2022 A subset $T$ of the vertex set of a network $G$ is called a resolving set for $G$ if each pair of vertices of $G$ have distinct representations with respect to $T$ . A resolving set $B^{\prime} $ among all the resolving sets of a network $G$
Imtiaz Ali +2 more
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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
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Fault-tolerant edge metric dimension of certain families of graphs
AIMS Mathematics, 2021 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xiaogang Liu +3 more
openaire +5 more sources
Fault-Tolerant Metric Dimension and Applications: Zero-Divisor Graph of Upper Triangular Matrices
MathematicsGraph invariants play a crucial role in understanding the structural and combinatorial characteristics of graphs. The fault-tolerant metric dimension, as a significant graph invariant, finds applications in diverse areas such as robust network ...
Latif Abdelmalek Hanna +2 more
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Investigating the Metric and Fault-Tolerant Dimensions in Para-Line Network Topologies
AKCE International Journal of Graphs and CombinatoricsThe resolving set (RS) and metric dimension (MD) are critical concepts used in various fields such as computer networks, robot navigation, chemical structures, communication networks, transportation, and electric circuits.
M. Faheem +5 more
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Fault-Tolerant Edge Metric Dimension of Zero-Divisor Graphs of Commutative Rings
AxiomsIn recent years, the intersection of algebraic structures and graph-theoretic concepts has developed significant interest, particularly through the study of zero-divisor graphs derived from commutative rings.
Omaima Alshanquiti +2 more
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On Fault-Tolerant Resolving Sets of Some Families of Ladder Networks
Complexity, 2021 In computer networks, vertices represent hosts or servers, and edges represent as the connecting medium between them. In localization, some special vertices (resolving sets) are selected to locate the position of all vertices in a computer network. If an
Hua Wang +4 more
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