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On the signed edge domination number of graphs

Akbari, S ; Sharif University of Technology | 2009

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  1. Type of Document: Article
  2. DOI: 10.1016/j.disc.2008.08.021
  3. Publisher: 2009
  4. Abstract:
  5. Let γs′ (G) be the signed edge domination number of G. In 2006, Xu conjectured that: for any 2-connected graph G of order n (n ≥ 2), γs′ (G) ≥ 1. In this article we show that this conjecture is not true. More precisely, we show that for any positive integer m, there exists an m-connected graph G such that γs′ (G) ≤ - frac(m, 6) | V (G) |. Also for every two natural numbers m and n, we determine γs′ (Km, n), where Km, n is the complete bipartite graph with part sizes m and n. © 2008 Elsevier B.V. All rights reserved
  6. Keywords:
  7. Complete bipartite graph ; m-connected ; Signed edge domination number ; 2-connected graphs ; Complete bipartite graph ; Connected graphs ; m-connected ; Natural numbers ; Positive integers ; Signed edge domination number ; Graph theory
  8. Source: Discrete Mathematics ; Volume 309, Issue 3 , 2009 , Pages 587-594 ; 0012365X (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/pii/S0012365X01000449