Abstract

Let S be a dominating set of G. A Decomposition G1, G2,…, Gn of G is said to be annihilator domination decomposition (add) if (i) E(G) = E(G1) ∪ E(G2) ∪ … ∪ E(Gn). (ii) In each Gi, 〈V(Gi)− S〉 has only isolated vertices, (iii) γadd (Gi) = i, 1 ≤ i ≤ n. In this paper we investigate annihilator domination decomposition of Banana tree graphs, Wheel graphs and Shell graphs.

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