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Signed edge domination numbers in trees

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 NG[e] of an edge e in a graph G is the set consisting of e and of all edges having a common endvertex with e. Let f be a function on E(G), the edge set of G, into the set {-1, 1}. If Σx∈N[e] f(x) ≥ 1 for each e ∈ E(G), then f is called a signed edge dominating function of G. The minimum of the values Σe∈E(G) f(e), taken over all 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(T) ≥ 1 for every tree T. In this paper we prove that this conjecture is true and then classify all trees T with γ′s(T) = 1, 2 and 3
  5. Keywords:
  6. Signed edge domination function; signed edge domination number ; Tree
  7. Source: Ars Combinatoria ; Volume 93, Issue 1 OCT , 2009 , Pages 451-457 ; 03817032 (ISSN)