On the local fractional metric dimension of corona product graphs

Aisyah, Siti; Utoyo, Mohammad Imam; Susilowati, Liliek

doi:10.1088/1755-1315/243/1/012043

Cited by 29 publications

(29 citation statements)

References 7 publications

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“…The resolving function is called local resolving function if η(R{uv}) ≥ 1. Similarly, FMD will become LFMD if we only consider the pair of adjacent vertices only, denoted by dim lf (N) [29].…”

Section: Preliminariesmentioning

confidence: 99%

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Local Fractional Metric Dimensions of Rotationally Symmetric and Planar Networks

2020

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Mathematical modeling, coding or labeling with the help of numeric numbers based on the parameter of distance plays a vital role in the studies of the structural properties of the networks such as accessibility, centrality, clustering, complexity, connectivity, modularity, robustness and vulnerability. In particular, various distance based dimensions of the networks are used to rectify the problems in different strata of computer science and chemistry such as navigation, image processing, pattern recognition, integer programming problem, drug discovery and formation of different chemical compounds. In this note, we consider a family of rotationally symmetric and planar networks called by circular ladders consisting of different faced triangles, quadrangles and pentagons. We compute local fractional metric dimensions of the aforesaid networks and study their boundedness. Moreover, our findings at the closure of this note have been summarized in the form of tables and 3-D plots. INDEX TERMS Fractional metric dimension, symmetric networks, resolving neighbourhoods.

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Section: Preliminariesmentioning

confidence: 99%

“…Recently, Aisyah et al (2019) defined the concept of local fractional metric dimension (LFMD) and computed it for the corona product of two networks [29]. In this note, we have considered a family of rotationally symmetric and planar networks called by circular ladders consisting of different faced triangle, quadrangle and pentagon.…”

Section: Introductionmentioning

confidence: 99%

Local Fractional Metric Dimensions of Rotationally Symmetric and Planar Networks

2020

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“…e resolving function will be a local resoling function if ϑ ′ (R s, t { }) ≥ 1 and the fractional metric dimension becomes a local fractional metric dimension (LFMD) if we assume the pair of adjacent vertices only; it is denoted by Dim lf (G) [20,28]. e LFMD of given graph in Figure 1 is Dim lf (G) ≤ (12/7).…”

Section: Preliminariesmentioning

confidence: 99%

“…e local fractional metric dimensions of planar networks were computed in [27]. In 2019, Aisyah et al introduced the concept of local fractional metric dimension (LFMD) and computed it for the corona product of two graphs [28]. Many researchers discussed this area in [5,6,8,[29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Classification of Upper Bound Sequences of Local Fractional Metric Dimension of Rotationally Symmetric Hexagonal Planar Networks

Ali

Mahmood

Tchier

et al. 2021

Journal of Mathematics

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The term metric or distance of a graph plays a vital role in the study to check the structural properties of the networks such as complexity, modularity, centrality, accessibility, connectivity, robustness, clustering, and vulnerability. In particular, various metrics or distance-based dimensions of different kinds of networks are used to resolve the problems in different strata such as in security to find a suitable place for fixing sensors for security purposes. In the field of computer science, metric dimensions are most useful in aspects such as image processing, navigation, pattern recognition, and integer programming problem. Also, metric dimensions play a vital role in the field of chemical engineering, for example, the problem of drug discovery and the formation of different chemical compounds are resolved by means of some suitable metric dimension algorithm. In this paper, we take rotationally symmetric and hexagonal planar networks with all possible faces. We find the sequences of the local fractional metric dimensions of proposed rotationally symmetric and planar networks. Also, we discuss the boundedness of sequences of local fractional metric dimensions. Moreover, we summarize the sequences of local fractional metric dimension by means of their graphs.

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“…min{|g| : g is a local minimal resolving function of N}. For more detail, see [1], [7], [14]. Now, we describe the methodology to compute LFMD of a connected network in the following points: (i) For each edge of the network, find LRN.…”

Section: Preliminariesmentioning

confidence: 99%

Sharp Bounds of Local Fractional Metric Dimensions of Connected Networks

2020

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Metric dimension is a distance based parameter which is used to determine the locations of machines (or robots) with respect to minimum consumption of time, shortest distance among the destinations and lesser number of the utilized nodes as places of the objects. It is also used to characterize the chemical compounds in the molecular networks in the form of their unique presentations. These are problems worth investigating in different strata of computer science and chemistry such as navigation, combinatorial optimization, pattern recognition, image processing, integer programming, network theory and drugs discovery. In this paper, a general computational criteria is established to compute the local fractional metric dimension (LFMD) of connected networks in the form of sharp lower and upper bounds. A complete characterization of the connected networks whose LFMDs attain the exactly lower bound is obtained and some particular classes of networks (complete networks, generalized windmill and h-level windmill) whose LFMDs attain the exactly upper bound are also addressed. In the consequence of the main obtained criteria, LFMDs of wheel-related networks (anti-web gear, m-level wheel, prism, helm and flower) are computed and their boundedness (or un-boundedness) is also illustrated with the help of 2D and 3D graphical presentations. INDEX TERMS Distance in networks; Metric dimension; Resolving neighborhood sets; Fractional metric dimension; Connected networks; Wheel-related networks.

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On the local fractional metric dimension of corona product graphs

Cited by 29 publications

References 7 publications

Local Fractional Metric Dimensions of Rotationally Symmetric and Planar Networks

Local Fractional Metric Dimensions of Rotationally Symmetric and Planar Networks

Classification of Upper Bound Sequences of Local Fractional Metric Dimension of Rotationally Symmetric Hexagonal Planar Networks

Sharp Bounds of Local Fractional Metric Dimensions of Connected Networks

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