Drawing Planar Graphs Symmetrically, II: Biconnected Planar Graphs

Symmetry is one of the most important aesthetic criteria in graph drawing because it reveals the structure in the graph. This paper discusses symmetric drawings of biconnected planar graphs. More specifically, we discuss geometric automorphisms, that is, automorphisms of a graph G that can be represented as symmetries of a drawing of G. Finding geometric automorphisms is the first and most difficult step in constructing symmetric drawings of graphs. The problem of determining whether a given graph has a non-trivial geometric automorphism is NP-complete for general graphs. In this paper we present a linear time algorithm for finding planar geometric automorphisms of biconnected planar graphs. A drawing algorithm is also discussed.