On (3, k)-Regular Fuzzy Graphs

In this paper, we defined d3-degree of a vertex in fuzzy graphs, total d3 -degree of a vertex in fuzzy graphs, (3, k) -regular fuzzy graphs and totally (3, k) - regular fuzzy graphs. (3, k) -regular fuzzy graphs and totally (3, k) -regular fuzzy graphs are compared through various examples. A necessary and sufficient condition under which they are equivalent is provided. Also, (3, k) -regularity on some fuzzy graphs whose underlying crisp graphs are a path on six vertices P6, a Corona graph Cn K1 (n5), a Wagner graph and a cycle Cn (n5) is studied with some membership function. Some properties of (3, k) -regular fuzzy graphs studied and they are examined for totally (3, k) -regular fuzzy graphs.