Abstract
A totally magic labeling of a graph with v vertices and e edges is a one-to-one map taking the vertices and edges onto the integers 1, 2, · · ·, v + e, such that the sum h of the label on a vertex and the labels on its incident edges is a constant independent of the choice of vertex, and the sum k of an edge label and the labels of the endpoints of the edge is constant. Such graphs appear to be rare. In this paper we examine the possible labelings of a union of an odd number of triangles, and determine the spectrum of possible values h, k for all known totally magic graphs. 1
Recommended Citation
McSorley, John P. and Wallis, Walter D. "On the Spectra of Totally Magic Labelings." Bulletin of the Institute of Combinatorics and Its Applications 37 (Jan 2003): 58-62.
