Let G be a connected graph in which we designate a vertex or a block (a biconnected component) as the center of G. For each cut-vertex v, let Gv be the connected subgraph induced from G by v and the vertices that will be separated from the center by removal of v, where v is designated as the root of Gv. We consider the set R of all such rooted subgraphs in G, and assign an integer, called an index, to each of the subgraphs so that two rooted subgraphs in R receive the same indices if and only if they are isomorphic under the constraint that their roots correspond each other. In this paper, assuming a procedure for computing a signature of each graph in a class of biconnected graphs, we present a framework for computing indices to all rooted subgraphs of a graph G with a center which is composed of biconnected components from . With this framework, we can find indices to all rooted subgraphs of a outerplanar graph with a center in linear time and space.