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In this paper we define smooth graceful labeling and we prove that cycle n C , complete bipartite graph n K 2, and path n P are… Expand For a connected graph G of order n ≥ 3, let f : E(G) → Zn be an edge labeling of G. The vertex labeling f ′ : V (G) → Zn induced… Expand This paper takes a close look at graceful labelling and its applications. We pay special attention to the famous Graceful Tree… Expand A Smarandache-Fibonacci Triple is a sequence S(n), n ≥ 0 such that S(n) = S(n−1)+S(n−2), where S(n) is the Smarandache function… Expand In this work some new odd graceful graphs are investigated. We prove that the graph obtained by joining two copies of even cycle… Expand It is easily shown that every path has a graceful labelling, however, in this paper we show that given almost any path P with n… Expand Several methods for breaking value symmetries have been proposed recently in the constraint programming community. They can be… Expand A graceful n-permutation is a graceful labeling of an n-vertex path P_n. In this paper we improve the asymptotic lower bound on… Expand A graph $G$ on $m$ edges is considered graceful if there is a labelling $f$ of the vertices of $G$ with distinct integers in the… Expand We establish that all trees on at most 27 vertices admit graceful labellings and all trees on at most 26 vertices admit… Expand