A graph is a collection of vertices (points) joined by edges (line segments). A pair of vertices are **adjacent** if they are connected by an edge.

Coloring a graph refers to assigning colors to its vertices. A graph is said to be **properly colored** if every pair of adjacent vertices receive different colors.

Consider the above graph with 4 vertices and 4 edges. This graph is denoted as \(C_{4} \). If you are permitted to use 6 different colors, how many proper coloring does \(C_{4} \) have ?

**Note:**

1. Vertices are adjacent if they are joined by an edge (line).

2.The coloring that is in the figure is an example of proper coloring.

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