Chromatic Partitioning of a Network and an Optimum Scheduling Problem

This article aims to study the chromatic polynomial of some families of graphs and to describe the properties of the chromatic polynomial of some graph operations. In addition, we will explore results related to a chromatic polynomial of the subgraph of path graph obtained after fusing two vertices that are at a finite distance. Also, we give an idea of optimum scheduling based on different color classes in the graph.