Distance-related invariants on polygraphs

Abstract

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 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.