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

  • Fuzzy systems and their mathematics
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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran

    M. Baghernejad

  2. Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran

    R. A. Borzooei

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  1. M. Baghernejad
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  2. R. A. Borzooei
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Correspondence to R. A. Borzooei.

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Baghernejad, M., Borzooei, R.A. Results on soft graphs and soft multigraphs with application in controlling urban traffic flows. Soft Comput 27, 11155–11175 (2023). https://doi.org/10.1007/s00500-023-08650-7

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