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Graph theory has been used to model some systems. Graph and fuzzy set have led to the concept of fuzzy graph. An Autocatalytic Set (ACS) is a concept formally introduced in chemistry as a set of catalytically integrated molecules. Fuzzy Autocatalytic Set (FACS) is a merge between fuzzy, graph and autocatalytic set (ACS). In this paper, some new characteristics on autocatalytic and fuzzy autocatalytic sets are presented. These characteristics are on possible paths in autocatalytic and fuzzy autocatalytic sets.doi:10.12732/ijpam.v115i1.4 fatcat:wqwnzcw6jffftlbues6n6e3334