The edge-graceful spectra of connected bicyclic graphs without pendant

Let G be a connected simple (p, q)-graph and k a non-negative integer. The graph G is said to be k-edge-graceful if the edges can be labeled with k, k + 1, . . . ,k + q – 1 so that the vertex sums are distinct modulo p. The set of all k where G is k-edge-graceful is called the edge-graceful spectrum of G. In 2004, Lee, Cheng and Wang analyzed the edge-graceful spectra of certain connected bicyclic graphs, leaving some cases as open problems. Here, we determine the edge-graceful spectra of all connected bicyclic graphs without pendant. Copyright © 2008 Charles Babbage Research Centre.