Abstract
In this paper , we define d 2 degree of a vertex in fuzzy graphs and total d 2 -degree of a vertex in fuzzy graphs and (2, k)-regular fuzzy graphs, totally (2, k) - regular fuzzy graphs are introduced. (2, k) - regular fuzzy graphs and totally (2, k)-regular fuzzy graphs are compared through various examples. A necessary and sufficient condition under which they are equivalent is provided. Also we provide a characterization of (2, k)-regular fuzzy graphs in which underlying crisp graph are a path on four vertices, a barbell graph of order 2n and a cycle. Some properties of (2, k)-regular fuzzy graphs studied and they are examined for totally (2, k)-regular fuzzy graphs
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