Domination integrity and efficient fuzzy graphs
| Autor: | Goksen Bacak-Turan, Sundareswaran Raman, Saravanan Mariappan, Sujatha Ramalingam |
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| Přispěvatelé: | Department of Mathematics, Mannar Thirumalai Naicker College, Pasumalai, Madurai, Tamil Nadu, India, Department of Mathematics, SSN College of Engineering, Old Mahabalipuram Road, Chennai, Tamil Nadu, India, Department of Mathematics, Celal Bayar University, Manisa, 45140, Turkey |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Discrete mathematics
Vertex (graph theory) 0209 industrial biotechnology Mathematics::General Mathematics Computer science Complete graph Stability (learning theory) 02 engineering and technology Cartesian product Fuzzy logic Tree (graph theory) Graph Vertex (geometry) symbols.namesake 020901 industrial engineering & automation Artificial Intelligence Dominating set Path (graph theory) 0202 electrical engineering electronic engineering information engineering symbols 020201 artificial intelligence & image processing Software MathematicsofComputing_DISCRETEMATHEMATICS |
| Popis: | In this paper, domination integrity of fuzzy graph and efficient fuzzy graph concepts is introduced with examples. An algorithm is developed to find whether an arc is strong or not. If it is strong, another algorithm will classify it as α strong arc and β strong arc. The next algorithm is used to find whether the given fuzzy graph is a fuzzy tree or not. Domination and integrity are two different parameters used to define the stability of a graph in various situations. Using the strong arc concept a new parameter, domination integrity is defined and lower and upper bounds are found. This paper discusses the domination integrity for standard graphs such as path, cycle and complete graph. The domination integrity for Cartesian product of fuzzy graphs is also discussed. Finally, the new class of fuzzy graph, efficient fuzzy graph, is introduced. Efficient fuzzy graph is a special type of fuzzy graph that has the same dominating set, other than vertex set V, for both fuzzy graph and its underlying crisp graph. © 2019, Springer-Verlag London Ltd., part of Springer Nature. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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