Description of Regular m-Bipolar Fuzzy Graphs

The first and second basic sequences in an m-BPFG are defined in this work along with an example of an adjacency sequence of a node. A few instances are created to demonstrate that, even if an m-BPFG is regular, the crisp underlying graph may or may not be regular or have a uniform adjacency sequence for all of the nodes. Additionally, it is demonstrated that not all of the nodes need to have the same adjacency sequence if an m-PPFG and its crisp underlying graph are regular. The notion of adjacency sequences is used to create a necessary and sufficient requirement for an m-BPFG to be regular if it has no more than four nodes. Along with, there are several definitions of what it means for a regular m-BPFG's complement, line graph, and other properties to be regular.