This study introduces and analyzes the conormal product of intuitionistic anti-fuzzy graphs (IAFGs) and analyzes certain fundamental theorems and applications. Further, new notions on complete and regular IAFGs were introduced, and the conormal product operation was applied to these IAFGs. We showed that the conormal product of two IAFGs could be used and analyzed important results showing that the conormal product of complete, regular, and strong IAFGs is an IAFG.

Fuzzy soft graphs are efficient numerical tools for simulating the uncertainty of the real world. A fuzzy soft graph is a perfect fusion of the fuzzy soft set and the graph model that is widely used in a variety of fields. This paper discusses a few unique notions of perfect fuzzy soft tripartite graphs (PFSTG), as well as the concepts of complement of perfect fuzzy soft tripartite graphs (CPFSTGs). Because soft sets are most useful in real-world applications, the newly developed concepts of perfect soft tripartite fuzzy graphs will lead to many theoretical applications by adding extra fuzziness in analysing. We look at some of their properties and come up with a few results that are related to these concepts. Furthermore, we investigated some fundamental theorems and illustrated an application of size of perfect fuzzy soft tripartite graphs in employee selection for an institution using the perfect fuzzy soft tripartite graph.