Affiliations:
Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan
Correspondence:
[*]
Corresponding author. Muhammad Akram, Department of Mathematics, University of the Punjab, New Campus, Lahore,
Pakistan. E-mail: makrammath@yahoo.com.
Abstract: Connectivity incorporates a significant role in various abstract and applied mathematical modeling and decision analysis. Graphical networks can be studied more precisely in connection with directed influenced flows, emphasizing the need of a mathematical approach for connectivity analysis. Our main focus in this research study is to generalize the concept of connectivity of fuzzy graphs to rough fuzzy digraphs (RFDs). We introduce the strength of connectedness between vertices, present different types of arcs in RFDs and investigate their properties. Moreover, we discuss the measures of connectivity, connectivity index, average connectivity index and isomorphism properties of partial rough fuzzy subdigraphs and spanning rough fuzzy subdigraphs. We apply various measures of connectivity to real world networks and with the help of connectivity reducing vertices, connectivity enhancing vertices and neutral vertices, we identify the most effective countries for human trafficking. Finally, we design an algorithm to describe the method discussed in the real world problem.
Keywords: Rough fuzzy digraph, strength of connectedness, connectivity index, average connectivity index. Mathematics Subject Classification 2010: 03E72, 68R10, 68R05
