TOTALLY MAGIC INJECTIONS
Abstract: A labelling is a
mapping whose domain is some set of graph elements | the set of vertices, for
example, or the set of all vertices and edges | and whose range is a set of
positive integers. In particular, if the labels associated with any edge { the
label on the edge itself, and those on its endpoints | always add to the same sum,
the labeling, and the graph possessing it, is called magic. A related concept,
a vertex-magic total labeling, is one in which the sum of the label on any
vertex with the labels on the edges containing it is always constant. A
labeling which has both the vertex-magic and edge-magic properties (usually
with two different constants) is called totally magic, as is a graph possessing
such a labeling. In this paper we survey what is known about totally magic
graphs and an important generalization.
Author: W. D. Wallis
Journal Code: jpmatematikagg110007
