• 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 Cn ͦ K1 (n≥5), a Wagner graph and a cycle Cn (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.
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