According to my approach, first color High degree vertices....
prepare a stack push the elements into ascending order of their degree's
i.e., high degree vertices is the top of the stack
the order we have to color is c,b,a,d,e,f may be permutation lead to any of 2*4!=48. take any one.
first color all vertices with c1
let pop one high degree vertex ( vertex c ) , color all its adjacent vertices to c2
let pop one more high degree vertex ( vertex B ), color all its adjacent vertices which are conflicting ( which are in the stack only by this property we can not disturb previously allocated colors to vertices which are high degree than currently poped vertex ) to c3.
continue this process until there is conflict.