Abstract
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). An equitable dominating set D is called a total equitable dominating set if the induced subgraph < D > has no isolated vertices. The total equitable domination number γte(G) of G is the minimum cardinality of a total equitable dominating set of G. If γte(G) ≠ |V(G)| and <G-E0> contains no isolated vertices then the total equitable bondage number bte(G) of a graph G is the minimum cardinality among all sets of edges E0 ⊆ E(G) for which γte(G-E0) > γte(G). In the present work we prove some characterizations and investigate total equitable bondage number of Ladder and degree splitting of path.
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