Total Equitable Bondage Number of a Graph

Abstract

If for any total dominating set D with v∈V(G) - D there exists a vertex u ∈ D such that uv∈E(G) and |d(v) - 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 γte (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 γG - E0γ(G). We introduced the concept of total equitable bondage number and proved several results.