Distance-related invariants on polygraphs Original Research Article

Let M(n) be a graph which is obtained from a path Pn or a cycle Cn by replacing each vertex by a fixed graph M and replacing each edge by a fixed set of edges joining the corresponding copies of M. A matrix approach to the computation of distance-related 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 detail.