Note:For C++ languages, the memory limit is 100 MB.For other languages, the memory limit is 200 MB. In graph theory, an independent set is a set of nonadjacent vertices in a graph. Moreover, an independent set is maximum if it has the maximum cardinality across all independent sets in a graph. An induced subgraph G' of a graph G is a graph that satisfies: * V′VV' subseteq VV′V * edge (a,b)∈E′(a,b) in E'(a,b)∈E′ if and only if a∈V′,b∈V′a in V', b in V'a∈V′,b∈V′, and edge (a,b)∈E in E(a,b)∈E; Now, given an undirected unweighted graph consisting of n vertices and m edges. This problem is about the cardinality of the maximum independent set of each of the 2n2^n2n possible induced subgraphs of the given graph. Please calculate the sum of the 2n2^n2n such cardinalities.
Note: For C++ languages, the memory limit is 100 MB. For other languages, the memory limit is 200 MB. In graph theory, an independent set is a set of nonadjacent vertices in a graph. Moreover, an independent set is maximum if it has the maximum cardinality (in this case, the number of vertices) across all independent sets in a graph. An induced subgraph G'(V', E') of a graph G(V, E) is a graph that satisfies: * V′⊆VV' subseteq VV′⊆V * edge (a,b)∈E′(a,b) in E'(a,b)∈E′ if and only if a∈V′,b∈V′a in V', b in V'a∈V′,b∈V′, and edge (a,b)∈E(a, b) in E(a,b)∈E; Now, given an undirected unweighted graph consisting of n vertices and m edges. This problem is about the cardinality of the maximum independent set of each of the 2n2^n2n possible induced subgraphs of the given graph. Please calculate the sum of the 2n2^n2n such cardinalities.
