ALGEBRAIC SPECIFICATION OF INTERCONNECTION NETWORK RELATIONSHIPS BY PERMUTATION VOLTAGE GRAPH MAPPINGS

Symmetries of large networks are used to simplify the specification of a guest-host network relationship. The relevant kinds of symmetries o ccur not only in Cayley graphs and in group-action graphs, but elsewhe re as well. In brief, the critical topological symmetry property of a guest or host is that it is algebraically specifiable as a covering sp ace of a smaller graph, A first objective is to understand the circums tances under which a mapping (a.k.a. ''embedding'') between two base g raphs can be lifted topologically to a mapping between their respectiv e coverings, A suitable assignment of algebraic elements called ''perm utation voltages'' to a base graph for the intended host network facil itates the construction not only of the intended host, but also of the intended guest and of the intended mapping of the guest into the host . Explicit formulas are derived for measurement of the load, of the co ngestion, and of the dilation of the lifted mapping. A concluding exam ple suggests how these new formulas open the opportunity to develop op timization methods for algebraically specified guest-host mappings.