No 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 (VC) are known as VC problems. The classical graphs do not reflect the impact of vertex on the edge and such impact is reflected in fuzzy incidence graphs (FIGs). We used optimization technique in a trade using clique covering (CC) in FIGs. This article includes some basic definitions such as strength of clique, strength of path, strength of minimum clique (SMC), acceptable strength of path and acceptable strength of clique, robust number, minimum covering number of the clique, close measure, some examples and theorems in FIGs, and new strategy of optimization to characterize and solve facility point problems by adopting the CC application of FIGs 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 are also checked in FIGs.A mathematical model is defined and a real-life problem from a trade is solved keeping the fuzziness of the objects related to FIG.

A Road Traffic Accident (RTAs) is a major social and economic concern in many countries especially in a developing country like Pakistan. As almost all motorcycle riders in Pakistan are self-taught and a lack of proper driving education, trainings and a rider gain his riding experience through trial and error basis. Since the early 60s, attempts have been made to model rider behavior, improve rider safety, enhance training sessions and to provide basic education about traffic rules and regulations. In pursuance to that, understanding of a rider’s behavior and finding the factors contributing to a motorcycle accident, a questionnaire comprising of 31 demographic and accident analysis questions were asked from 1400 respondents in Peshawar, Pakistan and their responses were statistically analyzed using a statistical analysis software namely Stata (Version 12). This research mainly focuses on the study of a rider’s behavior and the identification of important variables that leads to a motorcycle accident. Based on the statistically analyzed results, recommendations to the concern department(s) on the mitigation of motorcycle crash accidents was made. Analysis shows that less experience riders, teen aged riders and high speed of a motorcycle contributes the most in occurrence of an accident.