Some \(k\)-fold edge-graceful labelings of \((p,p-1)\)-graphs (Q2747183)

A graph \(G=(V,E)\) is edge-graceful, when there is a numbering of the edges from 1 to \(|E|\), such that each vertex \(v\) has a different value for the term \(\sum_{\{v,w\}\in E} f(v,w)\). A \(k\)-fold multigraph is a graph obtained by replacing edges in a graph by \(k\) parallel edges. This paper investigates the edge-gracefullness of \(k\)-fold multigraphs, e.g., those derived from paths, combs, spiders, or graphs with \(|V|-1\) edges.