Contraction and domination in fuzzy graphs

Abstract

Fuzzy sets and logics is a true crowning achievement of the century. Among the variety of exemplary changes in science and technology, the concept of uncertainty played a significant role, which led to the development of fuzzy sets, which in turn helped in the transition from graph theory to fuzzy graph theory. This paper familiarizes an improved concept in fuzzy graphs, called contraction. Two types of contraction namely edge contraction and neighbourhood contraction are introduced. We developed these two concepts in fuzzy graphs and analyse its effect on domination number and edge domination number. Any research is meaningful only by its contribution to the society. The modern world and the field of networks are inseparable. We have applied our concept to a wired network problem.