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Join of two graphs admits a nowhere-zero 3-flow

Akbari, S ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1007/s10587-014-0110-0
  3. Abstract:
  4. Let G be a graph, and λ the smallest integer for which G has a nowherezero λ-flow, i.e., an integer λ for which G admits a nowhere-zero λ-flow, but it does not admit a (λ − 1)-flow. We denote the minimum flow number of G by Λ(G). In this paper we show that if G and H are two arbitrary graphs and G has no isolated vertex, then Λ(G ∨ H) ⩽ 3 except two cases: (i) One of the graphs G and H is K2 and the other is 1-regular. (ii) H = K1 and G is a graph with at least one isolated vertex or a component whose every block is an odd cycle. Among other results, we prove that for every two graphs G and H with at least 4 vertices, Λ(G ∨ H) ⩽ 3
  5. Keywords:
  6. Join of two graphs ; Minimum nowhere-zero flow number ; Nowhere-zero λ-flow
  7. Source: Czechoslovak Mathematical Journal ; Vol. 64, Issue. 2 , 2014 , pp. 433-446 ; ISSN: 00114642
  8. URL: http://link.springer.com/article/10.1007%2Fs10587-014-0110-0