# Structural properties of fuzzy graphs

Document Type: Research Paper

Authors

1 School of Mathematics and Statistics, Xidian University, Xi'an, 710071, Shaanxi, China

2 School of Information and Technology, Northwest University, Xi'an, 710069, Shaanxi, China

Abstract

Matroids are important combinatorial structures and connect close-ly
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.

Keywords

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