![]() ![]() Senthilkumar and Ponnappan analyzed the idea of strong support VC of FG using strong arc. Vinothkumar and Ramya introduced covering in operations on FGs. studied covering and paired domination in IFGs. Manjusha and Sunitha introduced covering, matching, and paired domination in FGs using strong edges. The credibility theory to find the minimum fuzzy weight edge cover in an FG was discussed by Ni in 2008. Please note that each effective edge is strong, but a strong edge need not be effective. According to this definition, for any FG without effective edges, the VC is an empty set. Somasundaram defined the notion of coverings in a smaller domain of effective edges using scalar cardinality. According to this definition, a VC in an FG G is a subset D of vertices so that for each effective arc there is at least one of the two end points in D. The concept of covering in FG was introduced by Somasundaram who defined VC and edge covering in FGs using effective edges and scalar cardinality. Some researchers have studied the concepts of graph structure. introduced some new concepts of the interval-valued intuitionistic fuzzy graph (IVIFG). Talebi introduced Cayley fuzzy graphs to the fuzzy group. Some concepts of IFG were studied by Shao et al. ![]() conducted research on graphs and vague graphs. studied categorical properties of an intuitionistic fuzzy graph (IFG). Atanassov adopted the idea of an element membership and non-membership in a set and proposed the idea of intuitionistic fuzzy sets. Akram and Dudek presented the idea of an interval-valued fuzzy graph (IVFG) in 2011. Bhattacharya presented some observations on FGs and some operations on FGs were introduced by Mordeson and Peng. Bhutani and Rosenfeld introduced the concept of strong edges. This concept gained popularity with the introduction of the fuzzy set by Zadeh, and fuzzy graph (FG) by Rosenfeld, as they are characterized by two membership functions in for vertices and edges of a graph. Finally, two applications of strong vertex covering and strong vertex independence are presented.įuzzy theory is one of the best and most powerful tools for modeling problems in examining the relationships among uncertainties in the real world. Since many of the problems ahead are of hybrid type, by reviewing some operations on the cubic graph we were able to determine the strong vertex covering number on the most important cubic product operations. This issue can play a decisive role in covering the graph vertices. One of the motives of this research was to examine the changes in the strong vertex covering number of a cubic graph if one vertex is omitted. In this study, we introduced the strong vertex covering and independent vertex covering in a cubic graph with strong edges and described some of its properties. The previous definition limitations in the vertex covering of fuzzy graphs has directed us to offer new classifications in terms of cubic graph. The vertex cover is a fundamental issue in graph theory that has wide application in the real world. Simultaneous application of fuzzy and interval-valued fuzzy membership indicates a high flexibility in modeling uncertainty issues. The cubic graph, which has recently gained a position in the fuzzy graph family, has shown good capabilities when faced with problems that cannot be expressed by fuzzy graphs and interval-valued fuzzy graphs. ![]() Fuzzy graphs have the ability to solve uncertain and ambiguous problems. Graphs serve as one of the main tools for the mathematical modeling of various human problems.
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