D-MAGIC LABELING FOR TREES - Bagus Gede Baskara S, Ida
Let G = (V (G),E(G)) be a finite, simple, and undirected graph with n vertices. For a vertex u ? V (G), a set ND(u) = {v ? V (G) : d(u, v) ? D} is called the neighbourhood of distance D of u. A bijection f : V (G) ? {1, 2, ..., n} is called the D-magic labeling of G if there is a k such that P v?ND(u) f(v) = k for every u ? V (G). The main objective of this final project is to determine D-magic labelings for trees, in particular for paths, caterpillars, lobsters, and perfect binary trees.