## Authors

• Fahad Ur Rehman University of Management and Technology, Pakistan https://orcid.org/0000-0002-2600-5315
• Tabasam Rashid University of Management and Technology, Pakistan
• Muhammad Tanveer Hussain University of Management and Technology, Pakistan

## Keywords:

fuzzy incidence graphs, strength of clique, clique covering number, robust number and optimization in fuzzy incidence graph

## Abstract

In classical graph theory, set of vertices in which every edge is incident to at least one of the vertex is called a vertex covering set and the problems of vertex covering (V C) are known as V C problems. The classical graphs do not reflflect the impact of vertex on the edge and such impact is reflflected in fuzzy incidence graphs (F IGs). We used optimization technique in a trade using clique covering (CC) in fuzzy incidence graphs (F IGs). This article includes, some basic defifinitions such as strength of clique(SC), strength of path (SP), strength of minimum clique (SMC), acceptable strength of path (ASP) and clique (ASC), robust number (RN), minimum covering number of the clique (MCNC), close measure CM, some examples and theorems in F IGs, new strategy of optimization to characterize and solve facility points problems by adopting the CC application of F IGs for a business alliance to get maximum total achievement by reducing the transportation cost. This procedure will be helpful to develop sustainable economic developmental goal of the world. Some already existing theorems in fuzzy graphs (F Gs) are also checked in F IGs. A mathematical model is defifined and a real life problem from a trade is solved keeping the fuzziness of the objects related to fuzzy incidence graph.

Received: 22 February 2022 | Revised: 14 March 2022 | Accepted: 24 March 2022

Conflicts of Interest

The authors declare that they have no conflicts of interest to this work.

2022-03-28

## How to Cite

Rehman, F. U. ., Rashid, T. ., & Hussain, . M. T. (2022). Optimization in Business Trade by Using Fuzzy Incidence Graphs. Journal of Computational and Cognitive Engineering, 2(3), 196–203. https://doi.org/10.47852/bonviewJCCE2202176

## Section

Research Articles