here chromatic no. is always is equal to 4 because in this graph there is a complete graph K4 .and we know that a complete graph is n- colorable.and if we select any vertex randomly then we can say that it is 4- colorable.
total no. of different labeling =
1.selection of 1 vertex at a time out of 8 vertex =$\binom{8}{1}$=8.
2.four colors can be arranged in 4! ways =24.
so, total no. different labeling = 8*24=192.
am i correct?
