The chromatic index of a graph is the smallest number of colors needed to color the edges of the graph so that no two adjacent edges share the same color. This concept is important in graph theory, a branch of mathematics that studies the properties of graphs, which are structures made up of vertices (or nodes) connected by edges. Determining the chromatic index can be complex, especially for non-bipartite graphs. A well-known result related to this is Vizing's Theorem, which states that the chromatic index of a simple graph is either equal to its maximum degree or one more than that degree.