Types of arcs in a fuzzy graph |
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Authors: | Sunil Mathew M.S. Sunitha |
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Affiliation: | a Department of Mathematics, Government Brennen College, Thalassery, Kannur 670 106, India b Department of Mathematics, National Institute of Technology Calicut, NITC P.O, Calicut, Kerala 673 601, India |
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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 α-strong, β-strong and δ-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 α-strong, β-strong and δ-arcs. An arc of a fuzzy tree is α-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. |
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Keywords: | Strong arc Fuzzy bridge Fuzzy cutnode Fuzzy tree Complete fuzzy graph |
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