Edge-sum distinguishing labeling

04/15/2018

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by   Jan Bok, et al.

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In this paper we study edge-sum distinguishing labeling, a type of labeling recently introduced by Tuza tuza2017graph in context of labeling games. An ESD labeling of an n-vertex graph G is an injective mapping of integers 1 to l to its vertices such that for every edge, the sum of the integers on its endpoints is unique. If l equals to n, we speak about a canonical ESD labeling. We focus primarily on structural properties of this labeling and show for several classes of graphs if they have or do not have a canonical ESD labeling. As an application we show some implications of these results for games based on ESD labeling. Also, we show that ESD labeling is closely connected to the well-known notion of the Sidon sequence and harmonious labeling.