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 γet (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.