Directed rough fuzzy graph with application to trade networking

Ahmad, Uzma; Nawaz, Iqra

doi:10.1007/s40314-022-02073-0

Cited by 11 publications

(9 citation statements)

References 33 publications

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“…Finally, using the identical human trafficking network [7], we conducted a comprehensive comparative analysis and comparison table by briefly describing the results for the connectivity index (CI), the Wiener index (WI), and the N CI of a DRFG. This study can be expanded to include (1)…”

Section: Discussionmentioning

confidence: 99%

“…Furthermore, they presented the concept of CI, average connectivity index (ACI), and associated findings in DRFGs. Ahmad and Nawaz [1] recently researched connectivity in DRFGs and generalized Menger's theorem of vertices and edges in DRFGs. Ahmad and Nawaz [2] introduced the Wiener index (distance-based index) of a DRFG and its application to organized crime in 2022.…”

Section: Introductionmentioning

confidence: 99%

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Connectivity index of directed rough fuzzy graphs and its application in traffic flow network

Ahmad

Nawaz

2023

Granul. Comput.

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The directed rough fuzzy graph (DRFG) is a fusion of rough and fuzzy theory, because it deals with incomplete and vague information simultaneously. Connection or the strength of connectivity (SC) is vital in the realm of circuits or networks that are linked to the real world. As a result, SC is one of the most essential aspects of a directed rough fuzzy network system. The neighborhood connectivity index (N CI) is one such parameter that has a variety of applications in network theory. In this paper, we discuss the notion of N CI in DRFGs using the strength of vertices to their neighbor vertices. We provide several lower and upper bounds on the N CI of DRFGs with reference to other graph invariants such as the number of vertices, edges, and degree distance. When we study N CI in operations for DRFGs with a large number of vertices, the degree of vertices in a DRFG provides a confusing picture. Therefore, a mechanism to determine the N CI for DRFG operations is needed. Therefore, generalized formulas for N CI of DRFGs obtained by operations such as union, composition, and Cartesian product are also developed. An algorithm for obtaining N CI of DRFGs is also proposed. In addition, an application of N CI of DRFGs in traffic flow networks was discussed to identify the busiest intersection using the proposed algorithm. Finally, we gave a complete comparative evaluation and analysis table for a similar human trafficking system, comparing the results for connectivity index (CI), Wiener index (WI), and N CI.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Connectivity index of directed rough fuzzy graphs and its application in traffic flow network

Ahmad

Nawaz

2023

Granul. Comput.

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“…Ali et al [23] discussed the notion of t-connected fuzzy graphs and average fuzzy vertex connectivity. Ahmad and Nawaz [24] explored the application of connectivity in directed rough graphs for trade networking. Shang [25] introduced some asymptotic results on r-super connectedness for classical Erdos-Rényi random graphs as the number of nodes tends to infinity.…”

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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“…Different connectivity measures including connectivity index, Wiener index, domination number, topological indices, etc. are discussed in [15][16][17][18]. Measures of connectivity in rough fuzzy network models were studied by Akram and Zafar [19].…”

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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Directed rough fuzzy graph with application to trade networking

Cited by 11 publications

References 33 publications

Connectivity index of directed rough fuzzy graphs and its application in traffic flow network

Connectivity index of directed rough fuzzy graphs and its application in traffic flow network

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

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

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