Asymptotically optimal neighbour sum distinguishing colourings of graphs

  title={Asymptotically optimal neighbour sum distinguishing colourings of graphs},
  author={Jakub Przybylo},
  journal={Random Struct. Algorithms},
Consider a simple graph G = (V, E) and its proper edge colouring c with the elements of the set {1, 2, . . . , k}. The colouring c is said to be neighbour sum distinguishing if for every pair of vertices u, v adjacent in G, the sum of colours of the edges incident with u is distinct from the corresponding sum for v. The smallest integer k for which such colouring exists is known as the neighbour sum distinguishing index of a graph and denoted by χ∑(G). The definition of this parameter, which… CONTINUE READING
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