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A note on graceful graphs with large chromatic numbers

Mahmoody, A ; Sharif University of Technology | 2009

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  1. Type of Document: Article
  2. Publisher: 2009
  3. Abstract:
  4. A graceful labeling of a graph G with m edges is a function f : V(G) → {0,⋯, m} such that distinct vertices receive distinct numbers and {|f(u) - f(v)| : uv ∈ E(G)} = {1,⋯, m}. A graph is graceful if it has a graceful labeling. In [1] this question was posed: "Is there an n-chromatic graceful graph for n ≥ 6?". In this paper it is shown that for any natural number n, there exists a graceful graph G with χ(G) = n
  5. Keywords:
  6. Labeling ; Graph in graph theory ; Antimagic total
  7. Source: Ars Combinatoria ; Volume 90 , 2009 , Pages 423-424 ; 03817032 (ISSN)
  8. URL: http://www.combinatorialmath.ca/ArsCombinatoria/Vol90.html