Abstract
The lucky edge coloring of graph [Formula: see text] is a proper edge coloring which is induced by a vertex coloring such that each edge is labeled by the sum of its vertices. The least integer [Formula: see text] for which [Formula: see text] has a lucky edge coloring in the set [Formula: see text] is called lucky number, denoted by [Formula: see text]. The lucky numbers were already calculated for a large number of graphs, but not yet for trees. In this paper, we provide the characterization of lucky edge coloring and calculate the lucky number for graphs which can be regarded as complete [Formula: see text]-ary trees.
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