The chromatic number of a graph is the smallest number of colors needed to color its vertices so that no two adjacent vertices share the same color. This concept is important in graph theory, a branch of mathematics that studies the properties of graphs. The chromatic number helps in solving problems related to scheduling, map coloring, and resource allocation. To determine the chromatic number, one can use various algorithms and techniques, such as greedy coloring or backtracking. The chromatic number is denoted as χ(G) for a graph G. For example, a complete graph with n vertices has a chromatic number of n, as each vertex is connected to every other vertex.