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Super edge-graceful paths and cycles. (English) Zbl 1214.05149
Summary: A graph $$G(V,E)$$ of order $$|V|= p$$ and size $$|E|= q$$ is called super edge-graceful if there is a bijection $$f$$ from $$E$$ to $$\{0,\pm 1,\pm 2,\dots,\pm{q-1\over 2}\}$$ when $$q$$ is odd and from $$E$$ to $$\{\pm 1,\pm 2,\dots,\pm{q\over 2}\}$$ when $$q$$ is even such that the induced vertex labeling $$f^*$$ defined by $$f^*(x)= \sum_{xy\in E(G)} f(xy)$$ over all edges $$xy$$ is a bijection from $$V$$ to $$\{0,\pm 1,\pm 2,\dots, \pm{p-1\over 2}\}$$ when $$p$$ is odd and from $$V$$ to $$\{\pm 1,\pm 2,\dots, \pm{p\over 2}\}$$ when $$p$$ is even.
We prove that all paths $$P_n$$, except $$P_2$$ and $$P_4$$ and all cycles except $$C_4$$ and $$C_6$$ are super edge-graceful.
##### MSC:
 05C78 Graph labelling (graceful graphs, bandwidth, etc.) 05C38 Paths and cycles
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