Productive and sum graph labelings: A survey

Abstract

Graph labeling is one of the most popular and dynamic areas of graph theory, perhaps even among all of mathematics. The standard problem involves a graph having labels from a given set of integers on its vertices and then are assigned values according to some formula. Frank Harary introduced an alternative problem, in which the labels on the vertices themselves must meet a specified condition. Here, we give a survey of a problem of each type: (a) strongly multiplicative graphs, where, given a labeling of the vertices, each edge is labeled with the product of its vertex labels; (b) sum graphs, where, given a labeling of the vertices, two are adjacent if the sum of their labels is also a vertex label. © 2021 the authors.