Strong Perfect Cobondage Number of Standard Graphs

Abstract

Let G be a simple graph. A subset S Í V(G) is called a strong (weak) perfect dominating set of G if |N_s(u) ∩ S| = 1(|N_w(u) ∩ S| = 1) for every u ∊V(G) - S where N_s(u) = {v ∊ V(G) / uv  deg v ≥ deg u} (N_w(u) = {v ∊V(G) / uv  deg v ≤ deg u}. The minimum cardinality of a strong (weak) perfect dominating set of G is called the strong (weak) perfect domination number of G and is denoted by _sp(G)( _wp(G)). The strong perfect cobondage number bc_sp(G) of a nonempty graph G is defined to be the minimum cardinality among all subsets of edges X E(G) for which _sp (G + X) _sp(G). If bc_sp(G) does not exist, then bc_sp(G) is defined as zero. In this paper study of this parameter is initiated.