On (r,g)-Cages in Fuzzy Graphs

This paper introduces the concepts of girth of a fuzzy graph, [Formula: see text]-fuzzy graphs, [Formula: see text]-cages in fuzzy graphs, mono-cages, Moore-fuzzy graphs, and the corresponding Moore-fuzzy bounds. The study further establishes conditions under which Moore-fuzzy graphs exist. In particular, it shows that Moore-fuzzy graphs exist for any positive real number [Formula: see text] less than [Formula: see text] for arbitrary girth [Formula: see text], and for any positive real number [Formula: see text] greater than or equal to [Formula: see text] when the girth [Formula: see text] is [Formula: see text] or [Formula: see text].