Domination in fuzzy incidence graphs based on valid edges

• Published in: Journal of applied mathematics & computing Vol. 68; no. 1; pp. 101 - 124
• Main Authors: Afsharmanesh, S., Borzooei, R. A.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2022; Springer Nature B.V
• Subjects: Apexes; Applied mathematics; Computational Mathematics and Numerical Analysis; Fuzzy sets; Graph theory; Graphs; Mathematical and Computational Engineering; Mathematics; Mathematics and Statistics; Mathematics of Computing; Original Research; Theory of Computation; Incidence dominating set; Fuzzy incidence graphs; 05C72; Incidence independent set; Incidence irredundant set; 94C15; Incidence valid edges
• ISSN: 1598-5865; 1865-2085
• DOI: 10.1007/s12190-021-01510-3

Fuzzy graph theory provides tools for modeling different types of real-world networks. However, we should consider more relations, especially the relationship between edges with their corresponding vertices, which usually refer to incidences, when external factors influence the real flow in a network. Then, fuzzy incidence graphs may sometimes model certain real-world situations better. The present study aims to define incidence valid edges, the recognition of which is easy, and their number is more than that of effective edges. In this regard, we introduce dominating sets in fuzzy incidence graphs by using incidence valid edges due to the importance of the concept of domination and its application in various issues. In addition, several important sets related to the dominating set such as independent and irredundant sets are investigated. Further, the concepts of domination, upper domination, and independent domination number, as well as independence, irredundant, and upper irredundant number in fuzzy incidence graphs are evaluated, along with their relation. Finally, an application of the concept of domination in a fuzzy incidence graph is obtained.