Note on “Bipolar fuzzy graphs with applications”

摘要

In the paper, “Bipolar fuzzy graphs with applications” by Akram (2013), Definitions 3.2, 3.3, 3.4, 3.5, 4.3 and Theorem 3.16 contain some flaws. In this note, we show by examples that these definitions and theorem are not correct. The updated version of these definitions and theorem have been established in this paper with numerical examples.