#Domatic Number

def domatic_number(G, k):
    def is_dominating_set(G, S):
        # Check if S is a dominating set for G
        pass

    def backtrack(G, S, k, curr):
        if len(S) == k:
            if all(is_dominating_set(G, S[i]) for i in range(k)):
                return True
            else:
                return False
        for v in range(curr, len(G)):
            S.append(v)
            if backtrack(G, S, k, v+1):
                return True
            S.pop()
        return False

    min_domatic_number = float('inf')
    for k in range(k, len(G)):
        for S in itertools.combinations(range(len(G)), k):
            if backtrack(G, list(S), k, 0):
                min_domatic_number = min(min_domatic_number, k)
                break
    if min_domatic_number == float('inf'):
        return -1
    return min_domatic_number
