On (r,g)–Cages in Fuzzy Graphs
Priya Philip, Latha S. Nair
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Source: Crossref
Published: May 21, 2026
DOI: 10.1142/s179300572750075x
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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].
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