科研之友
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摘要
A graph G is anti-magic if there is a labelling of its edges with 1, 2,..., vertical bar E vertical bar such that the sum of the labels assigned to edges incident to distinct vertices are different. In this paper, we prove that if G is k-regular for k >= 2, then for any graph H with vertical bar E(H)vertical bar >= vertical bar V (H)vertical bar - 1 >= 1, the Cartesian product H square G is anti-magic. We also show that if vertical bar E(H)vertical bar >= vertical bar V(H)vertical bar - 1 and each connected component of H has a vertex of odd degree, or H has at least 2 vertical bar V(H)vertical bar - 2 edges, then the prism of H is anti-magic.
