Types of arcs in a fuzzy graph

The concept of connectivity plays an important role in both theory and applications of fuzzy graphs. Depending on the strength of an arc, this paper classifies arcs of a fuzzy graph into three types namely αα-strong, ββ-strong and δδ-arcs. The advantage of this type of classification is that it helps in understanding the basic structure of a fuzzy graph completely. We analyze the relation between strong paths and strongest paths in a fuzzy graph and obtain characterizations for fuzzy bridges, fuzzy trees and fuzzy cycles using the concept of αα-strong, ββ-strong and δδ-arcs. An arc of a fuzzy tree is αα-strong if and only if it is an arc of its unique maximum spanning tree. Also we identify different types of arcs in complete fuzzy graphs.