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International Conference on Statistics, Combinatorics and Related Areas and the Eighth International Conference of Forum for Interdisciplinary Mathematics
December 19-21, 2001
School of Mathematics and Applied Statistics, University of Wollongong
Wollongong, NSW, Australia

Organizers
Satya N. Mishra (University of South Alabama), Chandra M. Gulati (University of Wollongong)

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Sparse RC-Magic Squares and Magic Graph Labelings
by
James A. MacDougall
University of Newcastle
Coauthors: Ian D. Gray (University of Newcastle)

A *vertex-magic total labeling* of a graph (which has v vertices and e edges) assigns the numbers 1, 2,..., v+e to the vertices and edges so that at each vertex the sum of the vertex label and its incident edge labels is a constant. Among a number of methods for constructing such labelings, we have developed one which starts with a disconnected graph possessing a labeling and "glues" the components together by inserting appropriately labelled edges between them to produce a labeling for the resulting connected graph. This technique uses the entries from an array similar to a magic square, in which some of the entries can be 0's. We exhibit one method for constructing such arrays, which we call sparse RC-magic squares.

Date received: September 11, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cagd-74.