Lifting Graph Automorphisms by Voltage Assignments

The problem of lifting graph automorphisms along covering projections is considered in a purely combinatorial setting Because of certain natural ap plications and greater generality graphs are allowed to have semiedges This requires careful reexamination of the whole subject which leads to simpli ca tion and generalization of several known results For example Cayley graphs including those with involutory or repeated generators are characterized as regular coverings over one vertex graphs The ordinary and the permutation voltage constructions are uni ed into the concept of a voltage space constitut ing the crucial tool for combinatorialization of the lifting problem Particular attention is paid to the structure of lifted groups with focus on split extensions having a nice geometrical and combinatorial description Some applications of these results to regular maps on surfaces are given Supported in part by Ministrstvo za znanost in tehnologijo Slovenije proj no P Supported in part by VEGA grant no Supported in part by VEGA garnt no