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arXiv · 1701.00927

On neighbour sum-distinguishing $\{0,1\}$-edge-weightings of bipartite graphs

Kasper Szabo Lyngsie
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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 $w : E(G) \rightarrow S$ 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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Kasper Szabo Lyngsie. 2018-05-30. On neighbour sum-distinguishing $\{0,1\}$-edge-weightings of bipartite graphs. https://doi.org/10.23638/dmtcs-20-1-21

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