Edge-odd graceful labelings of some prism and prism-like graphs (Q2786887)

Given a graph \(G=(V,E)\) with \(q\) edges, an edge-odd graceful labeling is a bijection from \(V\) to \(\{1,3,\ldots, 2q-1\}\) such that when each vertex is assigned to the sum of the labels of all edges incident with it, all the vertex labels are different. In this paper, the authors give sufficient conditions for the following Cartesian products of graphs: \(S_n \square K_2\), \(S_n \square K_3\) and \(W_n \square K_2\), to have an edge-odd graceful labeling, where \(S_n\) is the star of order \(n+1\) and \(W_n\) is the wheel of order \(n+1\).