It is known that bipolar models give more precision, flexibility and compatibility to the system as compare to the classic and fuzzy models. A bipolar fuzzy graph can be obtained from two given bipolar fuzzy graphs using cartesian product and composition. In this paper, we have introduced the degree and total degree of an edge. Likewise, we found the degree of an edge in bipolar fuzzy graphs formed by these operations in terms of the degree of edges in the given bipolar fuzzy graphs in some particular cases. We defined μ-complement, self μ-complement, and self weak μ-complement on bipolar fuzzy graphs. Finally, we introduced an application of bipolar fuzzy digraphs.
AkramM., Bipolar fuzzy graphs, Information Sciences181 (2011), 5548–5564.
2.
BhattacharyaP., Some remarks on fuzzy graphs, Pattern Recognition Letters6 (1987), 297–302.
3.
JunY.B., Intuitionistic fuzzy subsemigroups and subgroups associated by intuitionistic fuzzy graphs, Commun Korean Math Soc21(3) (2006), 587–593.
4.
KauffmanA., Introduction a la Theorie des Sous Emsembles Flous, Vol. 1, Masson et Cie, 1973.
5.
MordesonJ.N. and PengC.S., Operations on fuzzy graphs, Information Sciences79 (1994), 159–170.
6.
MordesonJ.N. and NairP.S., Fuzzy Graphs and Fuzzy Hypergraphs, Physica, Heidelberg, Germany, 2nd edition. 2001.
7.
NagoorganiA. and RadhaK., The degree of a vertex in some fuzzy graphs, International journal of Algorithms, Computing and Mathematics2(3) (2009), 107–116.
8.
RosenfeldA., Fuzzy graphs, in Fuzzy Sets and Their Applications, ZadehL.A., FuK.S. and ShimuraM., Eds., Academic Press, New York, NY, USA, 1975, pp. 77–95.
9.
RashmanlouH. and JunY.B., Complete interval- valued fuzzy graphs, Annals of Fuzzy Mathematics and Informatics6(3) (2013), 677–687.
10.
RashmanlouH., SamantaS., PalM. and BorzooeiR.A., A study on bipolar fuzzy graphs, Journal of Intelligent and Fuzzy Systems28 (2015), 571–580.
11.
RashmanlouH., SamantaS., PalM. and BorzooeiR.A., Bipolar fuzzy graphs with categorical properties, International Journal of Computational Intelligent Systems8(5) (2015), 808–818.
12.
RadhaK. and KumaravelN., The degree of an edge in cartesian product and composition of two fuzzy graphs, International Journal of Applied Mathematics and Statistical Sciences2(2) (2013), 65–78.
13.
SamantaS. and PalM., Fuzzy tolerance graphs, Int J Latest Trend Math1(2) (2011), 57–67.
14.
SamantaS. and PalM., Bipolar fuzzy hypergraphs, International Journal of Fuzzy Logic Systems2(1) (2012), 17–28.
15.
SamantaS. and PalM., Fuzzy k-competition graphs and pcompetition fuzzy graphs, Fuzzy Engineering and Information5(2) (2013), 191–204.
16.
ZadehL.A., Fuzzy sets, Information and Control8(3) (1965), 338–353.
17.
ZhangW.R., Bipolar fuzzy sets, in: Proceedings of FUZZYIEEE (1998), 835–840.
