Shiu, W. C.; Ling, M. H.; Low, Richard M. The edge-graceful spectra of connected bicyclic graphs without pendant. (English) Zbl 1160.05041 J. Comb. Math. Comb. Comput. 66, 171-185 (2008). Summary: 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 \(k,k+1,\dots,k+q-1\) 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, S.-M. Lee, K.-J. Cheng and Y.-C. Wang [”On the edge-graceful spectra of cycles with one chord and dumbbell graphs,” Congr. Numeratium 170, 171–183 (2004; Zbl 1066.05131)] 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. MSC: 05C50 Graphs and linear algebra (matrices, eigenvalues, etc.) 05C78 Graph labelling (graceful graphs, bandwidth, etc.) 05C38 Paths and cycles Keywords:egde-graceful graph; edge-graceful spectra; Bicyclic graphs Citations:Zbl 1066.05131 PDFBibTeX XMLCite \textit{W. C. Shiu} et al., J. Comb. Math. Comb. Comput. 66, 171--185 (2008; Zbl 1160.05041)