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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| Published in | Soft computing (Berlin, Germany) Vol. 27; no. 16; pp. 11155 - 11175 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.08.2023
Springer Nature B.V |
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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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| AbstractList | 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. |
| Author | Borzooei, R. A. Baghernejad, M. |
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| Keywords | Degree Controlling urban traffic flows Size Soft multigraph Adjacency matrix Soft graph Complement Regularity |
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| References | Zadeh (CR30) 1975; 8 Baghernejad, Borzooei (CR8) 2019; 23 Blizard (CR10) 1988; 30 Khalili, Borzooei, Deldar (CR17) 2021; 67 Fathalian, Borzooei, Hamidi (CR14) 2019; 60 Roy, Maji (CR23) 2007; 203 CR15 Diestel (CR13) 2017 Maji, Roy, Biswas (CR18) 2001; 9 Afsharmanesh, Borzooei, Deldar (CR1) 2022; 68 Akram, Nawaz (CR4) 2016; 30 Thumbakara, George (CR25) 2014; 21 Tripathy, Arun (CR26) 2015; 7 Molodtsov (CR21) 1999; 37 Akram, Nawaz (CR3) 2015; 34 Aktas, Cagman (CR5) 2007; 177 Yager (CR28) 1986; 13 Wang, Zhan, Borzooei (CR27) 2017; 15 Baowen, Peizhuang, Xihui, Yong (CR9) 1988; 15 Borzooei, Almallah (CR12) 2022; 26 Bondy, Murty (CR11) 1976 Jean, Gosh, Tripathy (CR16) 2001; 132 Maji, Roy, Biswas (CR20) 2003; 45 Akram, Nawaz (CR2) 2015; 7 CR24 CR22 Zadeh (CR29) 1965; 8 Ali, Feng, Liu, Min, Shabir (CR6) 2009; 57 Babitha, Sunil (CR7) 2013; 5 Maji, Roy, Biswas (CR19) 2002; 44 M Akram (8650_CR4) 2016; 30 H Aktas (8650_CR5) 2007; 177 S Afsharmanesh (8650_CR1) 2022; 68 Q Wang (8650_CR27) 2017; 15 SP Jean (8650_CR16) 2001; 132 M Akram (8650_CR2) 2015; 7 RA Borzooei (8650_CR12) 2022; 26 M Fathalian (8650_CR14) 2019; 60 RR Yager (8650_CR28) 1986; 13 R Diestel (8650_CR13) 2017 BK Tripathy (8650_CR26) 2015; 7 DA Molodtsov (8650_CR21) 1999; 37 M Akram (8650_CR3) 2015; 34 PK Maji (8650_CR19) 2002; 44 MI Ali (8650_CR6) 2009; 57 KV Babitha (8650_CR7) 2013; 5 LA Zadeh (8650_CR30) 1975; 8 8650_CR15 M Khalili (8650_CR17) 2021; 67 PK Maji (8650_CR18) 2001; 9 AR Roy (8650_CR23) 2007; 203 RK Thumbakara (8650_CR25) 2014; 21 LA Zadeh (8650_CR29) 1965; 8 M Baghernejad (8650_CR8) 2019; 23 8650_CR22 PK Maji (8650_CR20) 2003; 45 8650_CR24 L Baowen (8650_CR9) 1988; 15 JA Bondy (8650_CR11) 1976 WD Blizard (8650_CR10) 1988; 30 |
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| SubjectTerms | 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 |
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| Title | Results on soft graphs and soft multigraphs with application in controlling urban traffic flows |
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