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Suppose we have a labelled graph G with vertices {1,2,3,...,n} and an
n-vector c of positive integers {c_1,c_2,c_3,...,c_n). Produce an
n-partite graph H by creating (for each i in {1,2,3,...,n}) a set T_i
containing c_i isolated vertices, and then joining every vertex in T_i
to every vertex in T_j whenever ij is an edge in G. So, each vertex i
in G corresponds to a set T_i in H, and each edge ij in G coresponds
to a collection of (c_i x c_j) edges in H.
What name is given to this type of structure?
TIA
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