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An improved upper bound for signed edge domination numbers in graphs

Karami, H ; Sharif University of Technology | 2009

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  1. Type of Document: Article
  2. Publisher: 2009
  3. Abstract:
  4. The closed neighborhood N G[e] of an edge e in a graph G is the set consisting of e and of all edges having a common end-vertex with e. Let f be a function on E(G), the edge set of G, into the set {-1, 1}. If σ xεN[e] f(x) ≥ 1 for each e ε E(G), Then f is called a signed edge dominating function of G. The minimum of the values of σ xεE(G) f(x), taken over every signed edge dominating function f of G, is called the signed edge domination number of G and is denoted by γ′ s(G). It has been conjectured that γ′ s(G) ≥ n - 1 for every simple graph G of order n. In this paper we prove that this conjecture is true for Eulerian simple graphs, simple graphs with all vertices of odd degree and regular graphs. As a result we prove that for any simple graph G of order n, γ′ s(G) ≥ [3n/2]. This improves theprevious upper bound [11n/6-l]
  5. Keywords:
  6. Signed edge dominating function ; Signed edge domination number
  7. Source: Utilitas Mathematica ; Volume 78 , 2009 , Pages 121-128 ; 03153681 (ISSN)