Types of arcs in a fuzzy graph

Authors:
Sunil Mathew;M. S. Sunitha
Affiliations:
Department of Mathematics, Government Brennen College, Thalassery, Kannur 670 106, India;Department of Mathematics, National Institute of Technology Calicut, NITC P.O, Calicut, Kerala 673 601, India
Venue:
Information Sciences: an International Journal
Year:
2009

Citing 13
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Abstract

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 @a-strong, @b-strong and @d-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 @a-strong, @b-strong and @d-arcs. An arc of a fuzzy tree is @a-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.