Intuitionistic fuzzy incidence graphs

Connectivity parameters have a crucial role in the study of different networks in the physical world. The notion of connectivity plays a key role in both theory and application of different graphs. In this article, a prime idea of connectivity concepts in intuitionistic fuzzy incidence graphs (IFIGs) with various examples is examined. IFIGs are essential in interconnection networks with influenced flows. Therefore, it is of paramount significance to inspect their connectivity characteristics. IFIGs is an extended structure of fuzzy incidence graphs (FIGs). Depending on the strength of a pair, this paper classifies three different types of pairs such as an alpha - strong, beta - strong, and delta-pair. The benefit of this kind of stratification is that it helps to comprehend the fundamental structure of an IFIG thoroughly. The existence of a strong intuitionistic fuzzy incidence path among vertex, edge, and pair of an IFIG is established. Intuitionistic fuzzy incidence cut pairs (IFICPs) and intuitionistic fuzzy incidence trees (IFIT) are characterized using the idea of strong pairs (SPs). Complete IFIG is defined, and various other structural properties of IFIGs are also investigated. The proof that complete IFIG does not contain any delta-pair is also provided. A real-life application of these concepts related to the network of different computers is also provided.

Automated summary

This article investigates the connectivity concepts in intuitionistic fuzzy incidence graphs (IFIGs) and provides various examples. By classifying pairs into different types based on their strength, the fundamental structure of IFIGs is thoroughly understood. The existence of a strong intuitionistic fuzzy incidence path in an IFIG is established. Additionally, the article explores other structural properties of IFIGs and applies the concepts to real-life computer networks.