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.

Source : oai:arXiv.org:1701.00927

DOI : 10.23638/DMTCS-20-1-21

Volume: Vol. 20 no. 1

Section: Graph Theory

Published on: June 4, 2018

Submitted on: January 5, 2017

Keywords: Mathematics - Combinatorics

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