Degree-Magic Labellings on Graphs Generalizing the Double Graph of the Disjoint Union of a Graph - Inpoonjai, Phaisatcha (Communications in Mathematics and Applications, 2021)
A graph \(G\) is called supermagic if it admits a labelling of the edges by pairwise different consecutive positive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. A graph \(G\) is called degree-magic if it admits a labelling of the edges by integers \(1,2,…,|E(G)|\) such that the sum of the labels of the edges incident with any vertex \(v\) is equal to \((1+|E(G)|)(v)/2\). In this paper, some constructions of degree-magic labellings of some graphs obtained by generalizing the double graph of the disjoint union of a graph are presented. As a result, some supermagic graphs are obtained.