On 2-partition dimension of the circulant graphs

Nadeem, Asim; Kashif, Agha; Zafar, Sohail; Zahid, Zohaib

doi:10.3233/jifs-201982

Cited by 12 publications

(5 citation statements)

References 29 publications

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“…Kamran et al computed the F(Ω) of homogeneous caterpillar, tadpole, and necklace graphs [2,4]. Asim et al computed F(Ω) of circulant graphs with connection set 1, 2 { } in [19]. In this paper, we extend this study by considering alternate triangular cycle, mirror graph, and tortoise graphs and show that they have constant fault-tolerant partition dimension.…”

Section: Introduction and Basic Terminologiesmentioning

confidence: 69%

Fault-Tolerant Partition Resolvability of Cyclic Networks

Azhar

Zafar

Kashif

et al. 2021

Journal of Mathematics

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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. Structure of web sites containing number of pages can be represented using graph, where web pages are considered to be the vertices, and an edge is a link between two pages. Figuring resolving partition of the graph is an intriguing inquest in graph theory as it has many applications such as sensor design, compound classification in chemistry, robotic navigation, and Internet network. The partition dimension is a graph parameter akin to the concept of metric dimension, and fault-tolerant partition dimension is an advancement in the line of research of partition dimension of the graph. In this paper, we compute fault-tolerant partition dimension of alternate triangular cycle, mirror graph, and tortoise graphs.

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Section: Introduction and Basic Terminologiesmentioning

confidence: 69%

Fault-Tolerant Partition Resolvability of Cyclic Networks

Azhar

Zafar

Kashif

et al. 2021

Journal of Mathematics

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“…For κ 2, the κ−partition dimension is known as fault tolerant partition dimension denoted by pd 2 (W). e pd 2 (W) was computed for some important networks in [15,16].…”

Section: Background and Related Workmentioning

confidence: 99%

On the Fault Tolerant Partition Resolvability of Toeplitz Networks

Nadeem

Kashif

Aljaedi

et al. 2022

Mathematical Problems in Engineering

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In any interconnection network, fault tolerance is the most desirable property to achieve reliability. Toeplitz networks are used as interconnection networks due their smaller diameter, symmetry, simpler routing, high connectivity, and reliability. The partition dimension of a network is presented as an extension of metric dimension of networks. Its applications can be seen in several areas including robot navigation, network designing, image processing, and chemistry. In this article, the fault tolerant partition dimension, pd 2 T n 1 , t , of Toeplitz networks, is shown to be bounded below by 4 for t ≥ 2 , n ≥ 4 , whereas it is bounded above by 5 for t = 3 , n ≥ 14 . Further, it is shown that the exact value of pd 2 T n 1 , t equals 4 for t = 2 , n ≥ 4 ; t = 3 , n ∈ 5,6 , … , 13 ; and t ≥ 4 , n ∈ t + 2 , t + 3 , t + 4 .

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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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On 2-partition dimension of the circulant graphs

Cited by 12 publications

References 29 publications

Fault-Tolerant Partition Resolvability of Cyclic Networks

Fault-Tolerant Partition Resolvability of Cyclic Networks

On the Fault Tolerant Partition Resolvability of Toeplitz Networks

Fault Tolerant Addressing Scheme for Oxide Interconnection Networks

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