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0-sum and 1-sum flows in regular graphs

Akbari, S ; Sharif University of Technology | 2016

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  1. Type of Document: Article
  2. Publisher: Australian National University , 2016
  3. Abstract:
  4. Let G be a graph. Assume that l and k are two natural numbers. An l-sum flow on a graph G is an assignment of non-zero real numbers to the edges of G such that for every vertex v of G the sum of values of all edges incident with v equals l. An l-sum k-flow is an l-sum flow with values from the set {±1,…, ±(k — 1)}. Recently, it was proved that for every r, r ≥ 3, r ≠ 5, every r-regular graph admits a 0-sum 5-flow. In this paper we settle a conjecture by showing that every 5-regular graph admits a 0-sum 5-flow. Moreover, we prove that every r-regular graph of even order admits a 1-sum 5-flow
  5. Keywords:
  6. 0-sum flow ; 1-sum flow ; Factor ; Regular graph
  7. Source: Electronic Journal of Combinatorics ; Volume 23, Issue 2 , 2016 ; 10778926 (ISSN)
  8. URL: http://www.combinatorics.org/ojs/index.php/eljc/article/view/v23i2p37