For any edge xy in a directed graph, the subtractive edge-weight is the sum of the label of xy and the label of y minus the label of x. Similarly, for any vertex z in a directed graph, the subtractive vertex-weight of z is the sum of the label of z and all edges directed into z and all the labels of edges that are directed away from z. A subtractive magic graph has every subtractive edge and vertex weight equal to some constant k. In this paper, we will discuss variations of subtractive magic labelings on directed graphs.
Ko, Matthew J.; Pinto, Jason; and Davis, Aaron
"New Results on Subtractive Magic Graphs,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 22:
1, Article 5.
Available at: https://scholar.rose-hulman.edu/rhumj/vol22/iss1/5