On neighbour sum-distinguishing \0,1\-edge-weightings of bipartite graphs
Abstract
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) → 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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