All regular graphs of small odd order are vertex-magic

This paper deals with vertex-magic total labellings of graphs. Earlier work by many authors has shown many infinite families of graphs to admit such labelings. The fact that many of these graphs are regular led MacDougall to conjecture that all non-trivial regular graphs are vertex-magic. Previously Gray and MacDougall showed that all odd-order r-regular graphs (r ≥ 2) of order up to v = 19 are vertex-magic. In this paper, we report on computations that extend this range, to show that all odd-order r-regular graphs (r ≥ 2) of order up to v = 29 are vertex-magic.