On regular power fuzzy graphs

In this paper, we define the notion of regular power fuzzy graph (RPFG), as a combination of regular properties and power fuzzy graphs. We also define totally regular power fuzzy graph as a special case of RPFG. A comparative study between regular and totally regular power fuzzy graphs is investigated. It is also proved that any power fuzzy graph containing a pendant vertex can be neither regular nor totally regular. A necessary condition for a total power fuzzy graph to be perfectly regular is that the vertex and edge membership functions are constants.