Geodesic
On neighbour sum-distinguishing $\{0,1\}$-edge-weightings of bipartite graphs
Discrete mathematics & theoretical computer science, Tome 20 (2018) no. 1.

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Let $S$ be a set of integers. A graph G is said to have the S-property if there exists an S-edge-weighting $w : E(G) \rightarrow S$ such that any two adjacent vertices have different sums of incident edge-weights. In this paper we characterise all bridgeless bipartite graphs and all trees without the $\{0,1\}$-property. In particular this problem belongs to P for these graphs while it is NP-complete for all graphs. 
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     title = {On neighbour sum-distinguishing $\{0,1\}$-edge-weightings of bipartite graphs},
     journal = {Discrete mathematics & theoretical computer science},
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Lyngsie, Kasper Szabo. On neighbour sum-distinguishing $\{0,1\}$-edge-weightings of bipartite graphs. Discrete mathematics & theoretical computer science, Tome 20 (2018) no. 1. doi : 10.23638/DMTCS-20-1-21. http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-20-1-21/

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