×

Super edge-magic labelings of generalized Petersen graphs \(P(n,3)\). (English) Zbl 1224.05470

A graph \(G\) of order \(n\) and size \(m\) is super edge-magic if there is a bijection \(f\: V(G)\cup E(G)\rightarrow \{1,2,\ldots ,m+n\}\) such that \(f(V(G))=\{1,2,\ldots ,n\}\) and there is a constant \(C\) such that \(f(u)+f(v)+f(uv)=C\) for any \(uv\in E(G)\). Y. Fukuchi [Ars Comb. 59, 253–257 (2001; Zbl 1066.05127)] proved that the generalized Petersen graph \(P(n,2)\) is super edge-magic for odd \(n\geq 3\). In the paper, it is shown that \(P(n,3)\) is super edge-magic for odd \(n\geq 5\).

MSC:

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

Citations:

Zbl 1066.05127
PDFBibTeX XMLCite