# Graph Theory Coloring Number

**A graph coloring is an assignment of labels called colors to the vertices of a graph such that no two adjacent vertices share the same color.**

**Graph theory coloring number**. In graph theory graph coloring is a special case of graph labeling. The minimum number of colors required for vertex coloring of graph g is called as the chromatic number of g denoted by x g. If g is not a null graph then χ g 2. Chromatic number of a graph is the minimum number of colors required to properly color the graph.

In its simplest form it is a way of coloring the vertices of a graph such that no two adjacent vertices are of the same color. It is impossible to color the graph with 2 colors so the graph has chromatic number 3. χ g 1 if and only if g is a null graph. This is called a vertex coloring.

This video discusses the concept of graph coloring as well as the chromatic number. If is odd then the last vertex would have the same color as the first vertex so the chromatic number will be 3. Graph coloring in graph theory graph coloring is a process of assigning colors to the vertices such that no two adjacent vertices get the same color. A graph coloring for a graph with 6 vertices.

But if it is even then first and last vertices will be of different color and the chromatic number will be 2. Solution if the vertex are colored in an alternating fashion the cycle graph requires 2 colors.