In the realm of linking networks to real world, connectivity (strength connectedness) plays a crucial role. this article, we introduce three types vertices based on indegree and outdegree directed rough fuzzy (DRFNs). We also define concept strength-reducing sets ( $$\mathcal {SRS}s$$ ) DRF-vertices, DRF-edges, important related results using strongest path in graphs (DRFGs). generalize idea Me...

A fuzzy graph can be obtained from two given fuzzy graphs using union and join. In this paper, we find the degree of an edge in fuzzy graphs formed by these operations in terms of the degree of edges in the given fuzzy graphs in some particular cases. 1. Introduction Fuzzy graph theory was introduced by Azriel Rosenfeld in 1975 [4]. Though it is very young, it has been growing fast and has nume...