An Introduction to Cyclic Path Covers in Graphs

This book is about the application of graph theory in studying the road traffic flow in a city. At any instance the aerial view of traffic flow of the city will appears like a connected graph, the roads and junction as edges and nodes respectively. In this situation, two mobile traffic cannot occupy a single junction (node of the graph) at the same instance. This is the motivation used in the development of Cyclic path cover. Usually a right driver will always choose a road which is having minimum number of traffic signals so that he needs unhindered flow of his vehicle irrespective of the distance. This is the underlying concept for the Cyclic Path covering number. Nowadays some of the junctions have flyovers so that the traffic is moving freely irrespective of junction. This flyover concept leads to the development of emvk-cyclic path covers. The one way traffics lead to the concept of directed graph in this same notion. Using the concept of cyclic path covering number, one can identify and use the best route (lengthy and economic due to fuel consumption) with least mental fatigue.