A STUDY ON (3, (c1, c2)) - REGULAR BIPOLAR FUZZY GRAPH

Abstract

In this paper, we defined d₃-degree of a vertex in bipolar fuzzy graphs, total d₃ -degree of a vertex in bipolar fuzzy graphs, (3, (c₁, c₂))-regular bipolar fuzzy graphs and totally (3, (c₁, c₂)) - regular bipolar fuzzy graphs. (3, (c₁, c₂))-regular bipolar fuzzy graphs and totally (3, (c₁, c₂))-regular bipolar fuzzy graphs are compared through various examples. A necessary and sufficient condition under which they are equivalent is provided. Also, (3, (c₁, c₂))-regularity on some bipolar fuzzy graphs whose underlying crisp graphs are a path on six vertices P₆, a Corona graph C_n  ͦ  K₁ (n≥5), a Wagner graph and a cycle C_n  (n≥5) is studied with some membership function. Some properties of      (3, (c₁, c₂))-regular bipolar fuzzy graphs studied and they are examined for totally (3, (c₁, c₂))-regular bipolar fuzzy graphs.