Certain types of graphs in interval-valued intuitionistic fuzzy setting

Abstract

Interval-valued intuitionistic fuzzy graph (IVIFG) as a generalization of intuitionistic fuzzy graph (IFG) increases its elasticity drastically. In this paper, some important types of IVIFGs such as regular, irregular, neighbourly irregular, highly irregular and strongly irregular IVIFGs are discussed. The relation among neighbourly irregular, highly irregular and strongly irregular IVIFGs is proved. The notion of intervalvalued intuitionistic fuzzy clique (IVIFC) is introduced. A complete characterization of the structure of the IVIFC is presented. Finally, an application of interval-valued intuitionistic fuzzy digraph (IVIFDG) in vulnerability assessment of water supply network is provided.