University of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065414120170228Structural properties of fuzzy graphs131144304810.22111/ijfs.2017.3048ENXiaonanLiSchool of Mathematics and Statistics, Xidian University, Xi'an, 710071,
Shaanxi, ChinaHuangjianYiSchool of Information and Technology, Northwest University, Xi'an,
710069, Shaanxi, ChinaJournal Article20151026Matroids are important combinatorial structures and connect close-ly<br />with graphs. Matroids and graphs were all generalized to fuzzy<br />setting respectively. This paper tries to study connections between<br />fuzzy matroids and fuzzy graphs. For a given fuzzy graph, we first<br />induce a sequence of matroids from a sequence of crisp graph, i.e.,<br />cuts of the fuzzy graph. A fuzzy matroid, named graph fuzzy matroid,<br />is then constructed by using the sequence of matroids. An equivalent<br />description of graphic fuzzy matroids is given and their properties<br />of fuzzy bases and fuzzy circuits are studied.http://ijfs.usb.ac.ir/article_3048_b36fae2bb90f788b2a7a140802ec8baa.pdf