Problem Encoding and Constraint Satisfaction

Assume that you are given a graph with $3$ vertices $(A,B,C)$ where every vertex is connected to every other vertex. The goal is to apply constraint

satisfaction to color the nodes of this graph with $2$ colors, $1$ and $2,$ so that no neighboring vertices have the same color.

Apply forward checking to this problem. To select variables, use the most constrained variable heuristic, breaking ties using the most constraining

variable heuristic. If ties still exist, break them in alphabetical order. To select values, use the least constraining value heuristic, and if ties exist, break

them in numeric order. Indicate the first $10$ branches visited in the search tree $($or stop when the solution is reached$).$

Format your answer such as $"A=2B=1"$ & $\text{'}$F$\text{'},$ similar to question $2.$

Answer:

$8$

$8$

&$.$

&$.$

$|$

&$.$

&

&$.$

$18$

QUESTION $6$

b$)$ Apply constraint propagation to eliminate values from the initial domains of the variables. Show the resulting domain of each variable after

constraint propagation is applied.

Shrw the dinmain as its elemante senarated by commas, e$.$g$."1,2".$ Put $"-"$ for empty domains.