Chromatic polynomial of a picture fuzzy graph with application in traffic light control

The fuzzy graph theory has many applications in solving various problems in multiple fields, including networking, communications, clustering, planning, and scheduling. In this article, we introduce the fundamental set of a picture fuzzy graph (PFG) and the ( θ , ρ , σ ) -level graph ( ( θ , ρ , σ )...

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Vydáno v:Journal of applied mathematics & computing Ročník 70; číslo 2; s. 1395 - 1418
Hlavní autoři: Abbas, Qamar, Mustafa, Ghulam
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2024
Springer Nature B.V
Témata:
Algorithms
Clustering
Computational Mathematics and Numerical Analysis
Decision making
Elections
Fuzzy sets
Graph theory
Graphs
Internet service providers
Mathematical and Computational Engineering
Mathematics
Mathematics and Statistics
Mathematics of Computing
Motorcycles
Original Research
Polynomials
Social networks
Theory of Computation
Traffic control
Traffic flow
Traffic signals
Vehicles
Fundamental set
03E72
05C78
05C99
Chromatic polynomial
05C72
Chromatic number
Application
Picture fuzzy graph
Level graph
ISSN:1598-5865, 1865-2085
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Popis
Shrnutí:The fuzzy graph theory has many applications in solving various problems in multiple fields, including networking, communications, clustering, planning, and scheduling. In this article, we introduce the fundamental set of a picture fuzzy graph (PFG) and the ( θ , ρ , σ ) -level graph ( ( θ , ρ , σ ) -LG) of a PFG, illustrating these concepts with an example. We then discuss the properties of the ( θ , ρ , σ ) -LGs of a PFG. Additionally, we introduce the concept of the chromatic polynomial (CP) of a PFG, providing a demonstration with an example using ( θ , ρ , σ ) -LGs of a PFG and exploring various properties of CP of a PFG. Furthermore, we construct an algorithm, which is executed using Matlab. This algorithm enables us to determine the number of distinct ways to colour a PFG with a specified number of colours. The application of the work presented is to answer the question: How does the picture fuzzy model propose to rectify the inefficiency in traffic signal timing where equal time is allocated to each vehicle in a flow based on vehicle count, leading to potential delays for vehicles with different characteristics, such as motorcycles and containers?
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1598-5865
1865-2085
DOI:10.1007/s12190-024-02011-9