A chromatic polynomial is a mathematical function that counts the number of ways to color the vertices of a graph using a given number of colors, ensuring that no two adjacent vertices share the same color. This concept is important in graph theory and helps in solving problems related to scheduling, map coloring, and network design. The chromatic polynomial, denoted as P(G, k) , depends on the graph G and the number of colors k . It can be computed using various methods, including the deletion-contraction method, which simplifies the graph by removing edges and vertices while preserving coloring properties.