what's the computational complexity of finding maximum common subconfiguration between several subgraph?

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given a set of subgraphs {G1,G2...,Gn} and another set {K1,K2...,Km}. Each G or K is a acyclic tree. Total vertices number in {G1,G2...,Gn} and {K1,K2...,Km} are equal. So, what's the computational complexity of finding maximum common subconfiguration between {G1,G2...,Gn} and {K1,K2...,Km}. In addition, the search begin at the center node of tree (root of tree) using DFS, if the edge is not equal the search of this branch will stop. image here

I think the computational complexity is O(n^2) between only 2 subgraphs. And i dont know what it is between several subgraphs.

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