## Abstract

A *total labeling* of a graph with *v * vertices and *e* edges is defined as a one-to-one map taking the vertices and edges onto the integers 1, 2, · · · , *v*+*e*. Such a labeling is *vertex magic* if the sum of the label on a vertex and the labels on its incident edges is a constant independent of the choice of vertex, and *edge magic* if the sum of an edge label and the labels of the endpoints of the edge is constant. In this paper we examine graphs possessing a labeling that is simultaneously vertex magic and edge magic. Such graphs appear to be rare.

## Recommended Citation

Exoo, Geoffrey, Ling, Alan C., McSorley, John P., Phillips, Nicholas C. and Wallis, Walter D. "Totally Magic Graphs." (Jun 2002).

## Comments

Published in

Discrete Mathematics, 254(1-3), 103-113.