Abstract
In this paper $d_{2}$- degree and total $d_{2}$-degree of a vertex in bipolar fuzzy graphs are defined. Also (2,($c_{1}$,$c_{2}$))-regularity and totally (2,($c_{1}$,$c_{2}$))-regularity of bipolar fuzzy graphs are defined. A relation between (2,($c_{1}$,$c_{2}$))-regularity and totally (2,($c_{1}$,$c_{2}$))-regularity on bipolar fuzzy graph is studied. (2,($c_{1}$,$c_{2}$))-regularity on path on four vertices, a Barbell graph $B_{m,n}$ (n$>$1) and a cycle $C_{n}$ are studied with some specific membership functions.
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