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Prime cordial labeling and duality. (English) Zbl 1269.05094

Let \(G\) be a graph and \(f\) be a bijection from its vertex set \(V\) to the set \(\{1,\dots,|V|\}.\) An edge \(uv\) in \(G\) is assigned a label \(1\) if \(\gcd (f(u),f(v)) = 1\) otherwise we label \(uv\) by \(0\). Then \(f\) is called prime cordial labeling if the number of edges labeled with \(1\) differs from the number of edges labeled by \(0\) by at most 1. The authors show that some very special classes of graphs posses prime cordial labeling.

MSC:

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