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Distance-based Invariants on Polygraphs

Let M (n) be a graph which is obtained from a path P n or a cycle C n by replacing each vertex by a xed graph M and replacing each edge by a xed set of edges joining the corresponding copies of M. A matrix approach to the computation of distance based invariants in such graphs is presented. This approach gives a general procedure to obtain closed formulas (depending on n) for such invariants of M (n). As an example, the Wiener index is treated in more details.