Intuitionistic fuzzy incidence graphs

Abstract

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 α - strong, β - strong, and δ-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 δ-pair is also provided. A real-life application of these concepts related to the network of different computers is also provided.