The main goal is to study the Hopf algebra structure on quivers. The main result obtained by C. Cibils and M. Rosso is improved. That is, in the case of infinite dimensional isotypic components it is shown that the path coalgebra kQ admits a graded Hopf algebra structure if and only if Q is a Hopf quiver. All nonisomorphic point path Hopf algebras and point co-path Hopf algebras are found. The ...

Unmanned aerial vehicles (UAVs), commonly known as drones, have drawn significant consideration thanks to their agility, mobility, and flexibility features. They play a crucial role in modern reconnaissance, inspection, intelligence, surveillance missions. Coverage path planning (CPP) which is one of the aspects that determines an intelligent system’s quality seeks optimal trajectory fully cove...

Abstract In the age of real-time online traffic information and GPS-enabled devices, fastest-path computations between two points in a road network modeled as directed graph, where each edge is weighted by “travel time” value, are becoming standard feature many navigation-related applications. To support this, very efficient computation these paths large networks critical. Fastest may be comput...