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On edge-graceful labelings of graphs. (English) Zbl 0597.05054
Proc. Conf., Sundance/Utah 1985, Congr. Numerantium 50, 231-241 (1985).
[For the entire collection see Zbl 0583.00003.] This paper is a further one dealing with labeling graphs. The author considers edge-graceful graphs being defined as follows: A connected graph $G=(V(G),E(G))$ is said to be edge-graceful if, and only if, there is an edge-labeling $g: E\to \{1,2,...,\vert (G)\vert \}$ of $G$ such that the weights $$w\sb g(v)=\sum\sb{e\in E(G), \ e \text{ incident to }v }g(e)\quad (\text{mod}\vert V(G)\vert)$$ for each vertex $v\in V(G)$ are consecutive integers ranging from 0 to $\vert V(G)\vert -1$. Analogously to the theory of the graceful graphs the author derives some properties of edge- graceful graphs, proves a necessary condition for a graph to be edge- graceful, determines some classes of edge-graceful graphs, and finishes with the conjecture: Each complete graph $K\sb p$ $(p\ge 2)$ is edge-graceful.
Reviewer: R. Bodendiek

05C99Graph theory