#Induced Connected Subgraph With Property ∏

from itertools import combinations

def induced_connected_subgraph_with_property(graph, property_function):
    def is_connected(subgraph, graph):
        visited = set()
        queue = [subgraph[0]]
        while queue:
            vertex = queue.pop(0)
            visited.add(vertex)
            for neighbor in graph[vertex]:
                if neighbor not in visited and neighbor in subgraph:
                    queue.append(neighbor)
        return len(visited) == len(subgraph)

    max_subgraph = []
    for vertex in graph:
        for subset in combinations(graph, vertex):
            if is_connected(subset, graph) and property_function(subset):
                if len(subset) > len(max_subgraph):
                    max_subgraph = subset
    return max_subgraph

def is_clique(subgraph):
    for vertex in subgraph:
        for neighbor in subgraph:
            if vertex != neighbor and neighbor not in graph[vertex]:
                return False
    return True

graph = {
    0: {1, 2},
    1: {0, 2},
    2: {0, 1, 3},
    3: {2},
    4: {5, 6},
    5: {4, 6},
    6: {4, 5}
}

induced_subgraph = induced

induced_connected_subgraph = induced_connected_subgraph_with_property(graph, is_clique)

print(induced_connected_subgraph)
