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Structural properties of fuzzy graphs. (English) Zbl 1368.05120
Summary: Matroids are important combinatorial structures and connect closely with graphs. Matroids and graphs were all generalized to fuzzy setting respectively. This paper tries to study connections between fuzzy matroids and fuzzy graphs. For a given fuzzy graph, we first induce a sequence of matroids from a sequence of crisp graph, i.e., cuts of the fuzzy graph. A fuzzy matroid, named graph fuzzy matroid, is then constructed by using the sequence of matroids. An equivalent description of graphic fuzzy matroids is given and their properties of fuzzy bases and fuzzy circuits are studied.
MSC:
05C72 Fractional graph theory, fuzzy graph theory
05B35 Combinatorial aspects of matroids and geometric lattices
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