Total Equitable Bondage Number of a Graph

Abstract

If for any total dominating set D with ν ∈ V (G) − D there exists a vertex u ∈ D such that uν ∈ E (G) and |d(ν)−d(u)| ≤ 1 then D is called the total equitable dominating set. The minimum cardinality of the total equitable dominating set is called the total equitable domination number denoted by γ^e_t (G). The bondage number b(G) of a nonempty graph G is the minimum cardinality among all sets of edges E₀ ⊆ E(G) for which γ(G – E₀) > γ(G). We introduced the concept of total equitable bondage number and proved several results.