The majority of early graph theory research on graph coloring pays attention only to find some possible solution to the Four
Color Conjecture. After Appel and Haken gave a computer verification proof of the Four Color Conjecture, research focus on
graph coloring was shifted to vertex coloring that satisfies some specified property for the induced edge coloring [5]. The
coloring is also played an important role in combinatorial optimization problems and critical graphs were crucial in the
Chromatic number Theory [7, 8, 9, 10, 11].
