Results on soft graphs and soft multigraphs with application in controlling urban traffic flows

In this paper, first we introduce the notions of size, order, and degree of vertices and edges in a soft graph, and we give some examples for a better understanding of these concepts. Then, we define the fundamental concepts of the adjacency matrix of soft graphs, complement of soft graphs, and regu...

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Bibliographic Details
Published inSoft computing (Berlin, Germany) Vol. 27; no. 16; pp. 11155 - 11175
Main Authors Baghernejad, M., Borzooei, R. A.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2023
Springer Nature B.V
Subjects
Apexes
Applied mathematics
Artificial Intelligence
Computational Intelligence
Control
Engineering
Fuzzy sets
Fuzzy Systems and Their Mathematics
Graph theory
Graphs
Mathematical Logic and Foundations
Mechatronics
Robotics
Traffic control
Traffic flow
Degree
Controlling urban traffic flows
Size
Soft multigraph
Adjacency matrix
Soft graph
Complement
Regularity
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Summary:In this paper, first we introduce the notions of size, order, and degree of vertices and edges in a soft graph, and we give some examples for a better understanding of these concepts. Then, we define the fundamental concepts of the adjacency matrix of soft graphs, complement of soft graphs, and regularity based on the degree of vertices of soft graphs, and we investigate some related results. Moreover, we introduce the concept of soft multiset and soft multigraph and define the notions of union, intersection, complement, and sum, and then we investigate the relations among them. Finally, we give an application of soft graphs in controlling urban traffic flows.
ISSN:1432-7643
1433-7479
DOI:10.1007/s00500-023-08650-7