# Strong edge-magic labelling of a cycle with a chord

MacDougall, James A. and Wallis, W. D. (2003) Strong edge-magic labelling of a cycle with a chord. Australasian Journal of Combinatorics, 28 . pp. 245-255. (In Press)

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Suppose G is a finite graph with vertex-set $V (G)$ and edge-set $E(G)$. An {\em edge-magic total labelling} on $G$ is a one-to-one map \lambda from V (G) \cup E(G) onto the integers 1, 2, . . . , $\mid V (G) \cup E(G)\mid$ with the property that, given any edge $(x,y)$, $$\lambda(x) + \lambda(x,y) + \lambda(y) = k$$ for some constant $k$. Such a labelling is called {\em strong} if the smallest labels appear on the vertices. In this paper, we investigate the existence of strong edge-magic total labellings of graphs derived from cycles by adding one chord.