Exact defensive alliances in graphs Article

Carballosa, W. (2013). Exact defensive alliances in graphs . Applied Mathematical Sciences, 7(73-76), 3673-3679. 10.12988/ams.2013.35244

cited authors

  • Carballosa, W

abstract

  • A nonempty set S ⊂ V is a defensive k-alliance in G = (V,E), k ∈ [-Δ, Δ] ∪ Z, if for every v ∈ S, dS(v) ≥ dS̄(v)+ k. A defensive k-alliance S is called exact, if S is defensive k-alliance but is no defensive (k+1)-alliance in G. In this paper we study the mathematical properties of exact defensive k-alliances in graphs. In particular, we obtain several bounds for defensive k-alliance of a graph. Furthermore, we characterize the exact defensive alliances in graph join G1 G2 in terms of G1, G2. © 2013 Walter Carballosa.

authors

publication date

  • July 31, 2013

published in

Digital Object Identifier (DOI)

start page

  • 3673

end page

  • 3679

volume

  • 7

issue

  • 73-76