Affiliations: [a]
Department of Mathematics, Shahid Beheshti University, Tehran, Iran
| [b]
Department of Mathematics, Islamic Azad University, Central Tehran Branch, Tehran, Iran
Correspondence:
[*]
Corresponding author. Hossein Rashmanlou, Department of Mathematics, Islamic Azad University, Central Tehran
Branch, Tehran, Iran. Tel.: +989384012972; Fax: +98 21 22431652; E-mail: [email protected].
Abstract: 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.
Keywords: Cartesian product, degree of an edge, total edge degree, µ–complement, self weak µ–complement
