Abstract
Given a graph G=(V,E) with two designated vertices s, t∈V, assign integer 1 to s and n=|V| to t, and {2,3,…,n-1} to V-{s,t} so that each vertex in V-{s,t} has at least one smaller neighbor and one larger neighbor. Such assignment is called an st-numbering. It is known that if G is biconnected then an st-numbering always exists, and an algorithm to find an st-numbering is known. In this paper we give a simple but efficient algorithm to enumerate all st-numberings of a given biconnected plane graph G with designated two vertices s and t on the outer face.
