Regularity parameters in intuitionistic fuzzy hypergraph and some domination in fuzzy graph

Abstract

Graph theory deals with the study of graphs, the mathematical structures which exhibit the relationship between the objects has extensive applications in diverse fields of science and technology. The rational theoretical framework of graph theory has laid the foundation of modelling the real life problems with the formulation of algorithms for computing optimal solutions to networking problems reflecting complex situations. This pragmatic approach made the researchers to extend the theory of graph to hypergraph, which is the generalization of graphs. The basic differences at conceptual level between the traditional graph and hypergraph theory is that a specific edge is between two nodes in a graph, however, in a hypergraph - the so called hyperedges - can group together more than two vertices. In the representation of graph an edge is drawn as a line, but in hypergraph edge is represented as a circle. The distinction between the graph and hypergraph stipulate dealing multifaceted problems involving multifarious structures. The process of translating a realistic problem to a mathematical form involves certain degree of participatory role of uncertainty, to handle such ambiguous situations, the notion of fuzzy has been integrated with graph theory and it is further extended to fuzzy hypergraph which is gaining momentum at recent times. This research work takes the study of fuzzy hypergraph to the next level of intuitionistic fuzzy hypergraph and this research study encircles around the investigation of the properties of regularity, irregularity of fuzzy hypergraph, intuitionistic fuzzy hypergraph, new generalized fuzzy hypergraph, intuitionistic fuzzy hypergraph. The property of pseudo regularity of fuzzy hypergraph, intuitionistic fuzzy hypergraph is investigated with special reference. This research work focuses on the expression of the pseudo degree for fuzzy hypergraph, generalized fuzzy hypergraph, intuitionistic fuzzy hypergraph and generalized intuitionistic fuzzy hypergraph so as to describe pseudo hypergra