Arc Types and Domination in Intuitionistic Fuzzy Graphs

Abstract

The theory of graph is an extremely useful tool for solving combinatorial problems in different areas such as geometry, algebra, number theory, topology, operations research, and optimization and computer science. In this paper, the definitions of strong arc, non- strong arc, semi \(\mu\)- strong arc, semi \(\rho\)- strong arc, effective arc, semi \(\mu\)-effective arc and semi \(\rho\)-effective arc of intuitionistic fuzzy graph. Further, the types of domination on intuitionistic fuzzy graph by for strong arc and effective arc are defined. Also the non-strong arc in intuitionistic fuzzy (IF) Path and IF Cycle are respectively compared with Fuzzy Path and Fuzzy cycle. Finally the relation between the effective arc domination and strong arc domination of IF graph with a suitable illustration is given. The strong arc domination and effective arc domination are discussed and it is concluded that the strong arc domination is always less than or equal to the effective arc domination.