Loading...

Some bounds for the signed edge domination number of a graph

Akbari, S ; Sharif University of Technology

5 Viewed
  1. Type of Document: Article
  2. Abstract:
  3. The closed neighbourhood NG[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 the edges of G into the set {-1, 1}. If ∑e∈NG[x] f(e) ≥ 1 for every x ∈ E(G), then f is called a signed edge domination function of G. The minimum value of ∑x∈E(G) f(x), taken over every signed edge domination function f of G, is called signed edge domination number of G and denoted by γ's (G). It has been proved that γ's(G) ≥ n - m for every graph G of order n and size m. In this paper we prove that γ's (G) ≥ 2α'(G)-m 3 for every simple graph G, where α'(G) is the size of a maximum matching of G. We also prove that for a simple graph G of order n whose each vertex has an odd degree, γ's(G) ≤ n - 2α(G) 3
  4. Keywords:
  6. Source: Australasian Journal of Combinatorics ; Volume 58, Issue 1 , 2014 , Pages 60-66 ; ISSN: 10344942
  7. URL: http://ajc.maths.uq.edu.au/pdf/58/ajc_v58_p060.pdf