Cubic Planar Graph and Its Application to Road Network

Muhiuddin, G.; Hameed, Saira; Rasheed, Ayman; Ahmad, Uzma

doi:10.1155/2022/5251627

Cited by 7 publications

(4 citation statements)

References 21 publications

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“…Muhiuddin et al [ 38 ] worked on cubic Pythagorean fuzzy graphs (CPFGs) and introduced certain fundamental operations such as semi-strong product, lexicographical product and symmetric difference of two CPFGs. Cubic planar graphs were investigated bu Muhiuddin et al [ 39 ]. They utilized it in road network problem.…”

Section: Introductionmentioning

confidence: 99%

Application of connectivity index of cubic fuzzy graphs for identification of danger zones of tsunami threat

Shi,

Kosari,

Hameed

et al. 2024

PLoS ONE

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Fuzzy graphs are very important when we are trying to understand and study complex systems with uncertain and not exact information. Among different types of fuzzy graphs, cubic fuzzy graphs are special due to their ability to represent the membership degree of both vertices and edges using intervals and fuzzy numbers, respectively. To figure out how things are connected in cubic fuzzy graphs, we need to know about cubic α−strong, cubic β−strong and cubic δ−weak edges. These concepts better help in making decisions, solving problems and analyzing things like transportation, social networks and communication systems. The applicability of connectivity and comprehension of cubic fuzzy graphs have urged us to discuss connectivity in the domain of cubic fuzzy graphs. In this paper, the terms partial cubic α−strong and partial cubic δ−weak edges are introduced for cubic fuzzy graphs. The bounds and exact expression of connectivity index for several cubic fuzzy graphs are estimated. The average connectivity index for cubic fuzzy graphs is also defined and some results pertaining to these concepts are proved in this paper. The results demonstrate that removing some vertices or edges may cause a change in the value of connectivity index or average connectivity index, but the change will not necessarily be related to both values. This paper also defines the concepts of partial cubic connectivity enhancing node and partial cubic connectivity reducing node and some related results are proved. Furthermore, the concepts of cubic α−strong, cubic β− strong, cubic δ−weak edge, partial cubic α−strong and partial cubic δ−weak edges are utilized to identify areas most affected by a tsunami resulting from an earthquake. Finally, the research findings are compared with the existing methods to demonstrate their suitability and creativity.

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Section: Introductionmentioning

confidence: 99%

Application of connectivity index of cubic fuzzy graphs for identification of danger zones of tsunami threat

Shi,

Kosari,

Hameed

et al. 2024

PLoS ONE

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“…Muhiuddin et al [50] worked on cubic Pythagorean fuzzy graphs (CPFGs) and introduced certain fundamental operations, such as the lexicographical product, semi-strong product, and symmetric difference of two CPFGs. Muhiuddin et al [51] discussed the concept of strong and weak edges for cubic planar graphs in 2022. In real-world scenarios, fuzzy graph ideas prove effective in describing certain phenomena, while interval-valued graph concepts excel in others.…”

Section: Introductionmentioning

confidence: 99%

Generalized connectivity in cubic fuzzy graphs with application in the trade deficit problem

Rao,

Chen,

Ahmad

et al. 2024

Front. Phys.

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Cubic fuzzy graphs (CFGs) offer greater utility as compared to interval-valued fuzzy graphs and fuzzy graphs due to their ability to represent the degree of membership for vertices and edges using both interval and fuzzy number forms. The significance of these concepts motivates us to analyze and interpret intricate networks, enabling more effective decision making and optimization in various domains, including transportation, social networks, trade networks, and communication systems. This paper introduces the concepts of vertex and edge connectivity in CFGs, along with discussions on partial cubic fuzzy cut nodes and partial cubic fuzzy edge cuts, and presents several related results with the help of some examples to enhance understanding. In addition, this paper introduces the idea of partial cubic α-strong and partial cubic δ-weak edges. An example is discussed to explain the motivation behind partial cubic α-strong edges. Moreover, it delves into the introduction of generalized vertex and edge connectivity in CFGs, along with generalized partial cubic fuzzy cut nodes and generalized partial cubic fuzzy edge cuts. Relevant results pertaining to these concepts are also discussed. As an application, the concept of generalized partial cubic fuzzy edge cuts is applied to identify regions that are most affected by trade deficits resulting from street crimes. Finally, the research findings are compared with the existing method to demonstrate their suitability and creativity.

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“…However, the traditional road network fractal dimension index can only be used to describe the relevant characteristics of a single level of road network in a specific area. Still, it cannot be effectively used for an overall road network including all levels of roads [20,21]. Therefore, it is necessary to seek an analysis process that can establish the relationship between different levels of roads and then integrate this process into the calculation of the traditional road network fractal dimension.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Road Networks Features of Urban Municipal District Based on Fractal Dimension

Deng

Wen

Zhang

2023

IJGI

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The structural characteristics of an urban road network directly affect the urban road network’s overall function and service level. Because the hierarchical division and layout form of an urban road network has self-similarity and scale invariance, the urban traffic network has certain time-space fractal characteristics, and fractal theory has become a powerful tool for evaluating traffic networks. This paper calculates and compares five fractal dimensions (FD) of nine districts in Harbin. Meanwhile, each calculated FD is linearly regressed with the area, population, built-up area, building area, the total number and length of roads, and the number of buildings in the region. The results show that the fractal dimensions of the five types are between 1 and 2. In the same district, the values of the FD perimeter and FD ruler are lower compared to the FD box, FD information, and FD mass, whereas those of the FD box and FD information are higher. Compared to the FD box and FD information, the value of FD mass shows unevenly. Based on the current research results, this study discusses the feasibility of using relevant indicators in the fractal process to evaluate the layout of the urban road network and guide its optimization and adjustment.

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Cubic Planar Graph and Its Application to Road Network

Cited by 7 publications

References 21 publications

Application of connectivity index of cubic fuzzy graphs for identification of danger zones of tsunami threat

Application of connectivity index of cubic fuzzy graphs for identification of danger zones of tsunami threat

Generalized connectivity in cubic fuzzy graphs with application in the trade deficit problem

Analysis of Road Networks Features of Urban Municipal District Based on Fractal Dimension

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