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On the super edge-magic deficiency of graphs. (English) Zbl 1164.05445

A graph \(G\) with \(p\) vertices and \(q\) edges is called edge-magic if there exists a bijective function \(f\: V(G)\cup E(G) \to \{1,2,\dots ,p+q\}\) such that \(f(u) + f(v) + f(uv) = k\) is a constant for any edge \(uv\in E(G)\). Moreover, \(G\) is said to be super edge-magic if \(f(V(G)) = \{1,2,\dots ,p\}\). The question studied in this paper is for which graphs it is possible to add a finite number of isolated vertices so that the resulting graph is super edge-magic.

MSC:

05C78 Graph labelling (graceful graphs, bandwidth, etc.)
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