Abstract
The notion of matching in a fuzzy graph could be defined using the concept of effective edges (8) or by fractional matching (4). In this paper, we derive a necessary condition for a fuzzy graph on a cycle or a complete graph or a stargraph to have a perfect fuzzy matching. Also we discuss perfect fuzzy matching on strong regular fuzzy graphs.
Highlights
Zadeh introduced the notion of Fuzzy sets and Fuzzy relations to deal with the problems of uncertainty in real physical world
In 1975, Rosenfeld [5] introduced the concept of fuzzy graphs
Using the concept of effective edges, Somasundaram [8] defined matching in a fuzzy graph
Summary
Zadeh introduced the notion of Fuzzy sets and Fuzzy relations to deal with the problems of uncertainty in real physical world. In 1975, Rosenfeld [5] introduced the concept of fuzzy graphs. Using the concept of effective edges, Somasundaram [8] defined matching in a fuzzy graph. This matching is defined only for those graphs having effective edges. Ramakrishnan P.V and Vaidyanathan M [4] introduced matching in a fuzzy graph using the concept of fractional matching. The notion of fractional matching given by Scheinerman [1], in 1997, involves the vertex weight, the edge weight and the incidence of Received: December 20, 2013 §Correspondence author c 2014 Academic Publications, Ltd. url: www.acadpubl.eu. We prove that a strong regular fuzzzy graph will have no perfect fuzzy matching
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