Affiliations: Department of Mathematics, Islamic Azad University, Central Tehran Branch, Tehran, Iran | Department of Mathematics, Joykrishnapur High School (H.S.), Tamluk, India | Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, India | Department of Mathematics, Shahid Beheshti University, Tehran, Iran
Note: [] Corresponding author. Hossein Rashmanlou, Department of Mathematics, Islamic Azad University, Central Tehran Branch, Tehran, Iran. E-mails: rashmanlou@gmail.com (Hossein Rashmanlou), ssamantavu@gmail.com (Sovan Samanta), mmpalvu@gmail.com (Madhumangal Pal), borzooei@sbu.ac.ir (Rajab Ali Borzooei).
Abstract: Recently, bipolar fuzzy graph is a growing research topic as it is the generalization of fuzzy graphs. In this paper, at first we define three new operations on bipolar fuzzy graphs, viz. direct product, semi strong product and strong product. Likewise, sufficient conditions for each one of them to be complete are given. Also, it is proved that any of the products of strong bipolar fuzzy graphs are strong bipolar fuzzy graphs.
Keywords: Bipolar fuzzy graph, direct product, strong product, ring sum
