On the Partition Dimension of Tri-Hexagonal α-Boron Nanotube

Shabbir, Ayesha; Azeem, Muhammad

doi:10.1109/access.2021.3071716

Cited by 45 publications

(18 citation statements)

References 36 publications

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“…When the specific values of moving parameters C 1 = C 2 = C 3 = 3, kekule is a part of hollow coronoid [35]. A pericondensed benzenoids structure which is known as circumcoronene also among the family of hollow coronoids [36]. A hollow coronoid, as depicted in Figure 1, had total 6 facets C 1 , C 2 , C 3 , C 4 , C 5 , C 6 .…”

Section: Construction Of Hollow Coronoidmentioning

confidence: 99%

Edge Metric and Fault-Tolerant Edge Metric Dimension of Hollow Coronoid

et al. 2021

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Geometric arrangements of hexagons into six sides of benzenoids are known as coronoid systems. They are organic chemical structures by definition. Hollow coronoids are divided into two types: primitive and catacondensed coronoids. Polycyclic conjugated hydrocarbon is another name for them. Chemical mathematics piques the curiosity of scientists from a variety of disciplines. Graph theory has always played an important role in making chemical structures intelligible and useful. After converting a chemical structure into a graph, many theoretical and investigative studies on structures can be carried out. Among the different parameters of graph theory, the dimension of edge metric is the most recent, unique, and important parameter. Few proposed vertices are picked in this notion, such as all graph edges have unique locations or identifications. Different (edge) metric-based concept for the structure of hollow coronoid were discussed in this study.

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Section: Construction Of Hollow Coronoidmentioning

confidence: 99%

Edge Metric and Fault-Tolerant Edge Metric Dimension of Hollow Coronoid

et al. 2021

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“…Some chemical compounds linked to wheel graphs, and also a comparison of metric and edge metric dimensions is discussed in [31]. Adding more to it, a few interesting studies related to metric dimension can be found in [32]- [36]. More related topics are discussed in [37]- [41].…”

Section: Introductionmentioning

confidence: 99%

Patched Network and Its Vertex-Edge Metric-Based Dimension

et al. 2023

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The p-type networks are designed with the help of CVNET at topo group Cluj and also given support by nano studio. Such networks develop new p-type surfaces and also represent the decorations of the surfaces. This patched network is designed by two repeated units. The first one is triphenylene having a Z-pen formula and the second one is triphenylene with A-phe. Furthermore, these decorations are acquired as the result of map operations represented in the CVNET software, while its assembling is conducted with the help of the nano studio program. In the literature, its topology is discussed by Omega polynomials which is an applied graph theory topic. Another most applied topic of graph theory is known as the resolvability parameter. So this article studied the resolvability parameters of patched networks, such as metric dimension, and edge metric dimension. These parameters are defined as a resolving set is a subset of vertices of a graph with a condition that each vertex of that graph has a unique code or representation with respect to the chosen subset. Its minimum cardinality is known as metric dimension, while the edge metric dimension is defined by the minimum count of members in the edge resolving set and this set is defined as according to a chosen subset each edge of a graph has unique representations, then this set is known as edge resolving set. A resolving set is a subset of vertices of a graph with a condition that each edge of that graph has a unique code or representation with respect to the chosen subset. It is minimum cardinality is known as the edge metric dimension.

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“…The concept of pd( ) for numerous classes of graphs has discussed extensively in literature. For instance, the PD of starphene graph was evaluated by Ahmad et al (see [3]), bridge graph by Amrullah et al (see [4]) and of tri-hexagonal α-boron nanotube by Ayesha et al (see [30]). The bounds on PD of generalized Mobius ladder were provided by Hussain et al (see [19]) and PD for certain classes of series parallel graph was studied by Monica et al (see [23]).…”

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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On the Partition Dimension of Tri-Hexagonal α-Boron Nanotube

Cited by 45 publications

References 36 publications

Edge Metric and Fault-Tolerant Edge Metric Dimension of Hollow Coronoid

Edge Metric and Fault-Tolerant Edge Metric Dimension of Hollow Coronoid

Patched Network and Its Vertex-Edge Metric-Based Dimension

Fault-Tolerant Partition Resolvability in Mesh Related Networks and Applications

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