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A note on zero-sum 5-flows in regular graphs

Akbari, S ; Sharif University of Technology

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  1. Type of Document: Article
  2. Abstract:
  3. Let G be a graph. A zero-sum flow of G is an assignment of non-zero real numbers to the edges of G such that the sum of the values of all edges incident with each vertex is zero. Let k be a natural number. A zero-sum k-flow is a flow with values from the set {±1,...,±(k - 1)}. It has been conjectured that every r-regular graph, r ≥ 3, admits a zero-sum 5-flow. In this paper we provide an affirmative answer to this conjecture, except for r = 5
  4. Keywords:
  5. Regular graph ; Zero-sum flow
  6. Source: Electronic Journal of Combinatorics ; Volume 19, Issue 2 , 2012 , Pages 1-5 ; 10778926 (ISSN)
  7. URL: http://www.combinatorics.org/ojs/index.php/eljc/article/view/v19i2p7