# Vertex-Magic Total Labelings of Wheels and Related Graphs

MacDougall, James A. and Miller, Mirka and Wallis, W. D. (2002) Vertex-Magic Total Labelings of Wheels and Related Graphs. Utilitas Mathematics, 62 . pp. 175-183.

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We prove the wheel $W_n$ has a vertex-magic total labeling if and only if $n \leq 11$. Corresponding results are found for wheels with multiple centres and several other generalizations of wheels. A complete enumeration of vertex-magic total labelings for the wheels $W_3$, $W_4$ and $W_5$ reveals unexpectedly large numbers.