ABSTRACT
A labeling graph labeling (or valuation) of a graph is a map that carries graph elements to numbers (usually to the positive or non-negative integers). The most common choices of domain are the set of all vertices and edges (such labelings are called total labelings), the vertex-set alone (vertex-labelings), or the edge-set alone (edge-labelings). In many cases, it is interesting to consider the sum of all labels associated with a graph label. This will be called the weight of the element. This chapter defines two labelings of the same graph to be equivalent if one can be transformed into the other by an automorphism of the graph. Magic squares are among the more popular mathematical recreations. Their origins are lost in antiquity. Various authors have introduced labelings that generalize the idea of a magic square.
