On the Fault Tolerant Partition Resolvability of Toeplitz Networks

Nadeem, Asim; Kashif, Agha; Aljaedi, Amer; Zafar, Sohail

doi:10.1155/2022/3429091

Cited by 6 publications

(3 citation statements)

References 11 publications

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“…The pd 2 (W) is termed as a fault tolerant partition dimension. The pd 2 (W) was computed for some important graphs in [6,[29][30][31][32][33][34]. Furthermore, the following lemma characterizes the graphs with a fault tolerant partition dimension bounded below by 4 and will be used in computing the fault tolerant partition dimension of SOXCN, RHOXN and RTOXN interconnection networks in the forthcoming subsections.…”

Section: Introductionmentioning

confidence: 99%

Fault Tolerant Addressing Scheme for Oxide Interconnection Networks

et al. 2022

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The symmetry of an interconnection network plays a key role in defining the functioning of a system involving multiprocessors where thousands of processor-memory pairs known as processing nodes are connected. Addressing the processing nodes helps to create efficient routing and broadcasting algorithms for the multiprocessor interconnection networks. Oxide interconnection networks are extracted from the silicate networks having applications in multiprocessor systems due to their symmetry, smaller diameter, connectivity and simplicity of structure, and a constant number of links per node with the increasing size of the network can avoid overloading of nodes. The fault tolerant partition basis assigns unique addresses to each processing node in terms of distances (hops) from the other subnets in the network which work in the presence of faults. In this manuscript, the partition and fault tolerant partition resolvability of oxide interconnection networks have been studied which include single oxide chain networks (SOXCN), rhombus oxide networks (RHOXN) and regular triangulene oxide networks (RTOXN). Further, an application of fault tolerant partition basis in case of region-based routing in the networks is included.

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Section: Introductionmentioning

confidence: 99%

Fault Tolerant Addressing Scheme for Oxide Interconnection Networks

et al. 2022

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“…The FTPD of denoted by F( ) is defined as the least number of subsets in set Y. Kamran et al provided the exact value of FTPD of homogeneous caterpillar (see [5]), cyclic networks (see [6]), tadpole and necklace graph (see [7]). Asim et al discussed FTPD of toeplitz networks and circulant graphs having {1, 2} connection set (see [25], [26]). In this paper we investigate the FTPD for two triangular mesh architectures derived from the standard triangular ladder.…”

Section: Introduction and Basic Terminologiesmentioning

confidence: 99%

Fault-Tolerant Partition Resolvability in Mesh Related Networks and Applications

et al. 2022

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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 each node in the presence of faults, having promising applications in telecommunication, robot navigation and geographical routing protocols. In this paper, certain triangular mesh networks including, triangular ladder (T l s ), triangular mesh (T s ) , reflection triangular mesh (rl(T s )), tower triangular mesh (T r s ) and reflection tower triangular mesh (rl(T r s )) networks are discussed for their partition and fault-tolerant partition resolvability. In this regard, it is shown that the partition dimension of these networks is 3, whereas their fault-tolerant partition dimension is 4.INDEX TERMS triangular ladder, triangular mesh, metric dimension, partition dimension, fault-tolerant partition dimension.

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“…Sharma and Bhat, in [22], calculated the FTMD of three families of the double antiprism graphs, which equals to 4. For more applications of the FTMD, see [23][24][25].…”

Section: Introductionmentioning

confidence: 99%

On the FAULT-TOLERANT Resolvability in Line Graphs of Dragon and Kayak Paddles Graphs

Faheem

Zahid

2022

Mathematical Problems in Engineering

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Because of its wide range of applications, metric resolvability has been used in chemical structures, computer networks, and electrical circuits. It has been applied as a node (sensor) in an electric circuit. The electric circuit will not be able to flow current if one node (sensor) in that chain becomes faulty. The fault-tolerant selfstable circuit is a circuit that permits the current flow even if one of the nodes (sensors) becomes faulty. If the removal of any node from a resolving set (RS) of the circuit is still a RS, then the RS of the circuit is considered a fault-tolerant resolving set (FTRS) and the fault-tolerant metric dimension (FTMD) is its minimum cardinality. Even though the problem of finding the exact values of MD in line graphs seems to be even harder, the FTMD for the line graphs was first discussed by Guo et al. [13]. Ahmad et al. [5] determined the precise value of the MD for the line graph of the kayak paddle graph. We calculate the precise value of the FTMD for the line graph in this family of graphs. The FTMD is a more generalized invariant than the MD. We also consider the problem of obtaining a precise value for this parameter in the line graph of the dragon graph. It is concluded that these families have a constant FTMD.

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On the Fault Tolerant Partition Resolvability of Toeplitz Networks

Cited by 6 publications

References 11 publications

Fault Tolerant Addressing Scheme for Oxide Interconnection Networks

Fault Tolerant Addressing Scheme for Oxide Interconnection Networks

Fault-Tolerant Partition Resolvability in Mesh Related Networks and Applications

On the FAULT-TOLERANT Resolvability in Line Graphs of Dragon and Kayak Paddles Graphs

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