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A new graph invariant called the secure vertex cover pebbling number, which is a combination of two graph invariants, namely, ‘secure vertex cover’ and ‘cover pebbling number’, is introduced in this paper. The secure vertex cover pebbling number of a graph, [Formula: see text], is the minimum number [Formula: see text] so that every distribution of [Formula: see text] pebbles can reach some secure vertex cover of [Formula: see text] by a sequence of pebbling moves. In this paper, the complexity of the secure vertex cover problem and secure vertex cover pebbling problem are discussed. Also, we obtain some basic results and the secure vertex cover pebbling number for complete [Formula: see text]-partite graphs, paths, Friendship graphs, and wheel graphs.

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A set S ⊆ V of vertices in a graph G = (V,E) is called a dominating set if every vertex in V − S is adjacent to a vertex in S. A dominating set which intersects every maximum independent set in G is called an independent transversal dominating set. In this paper we begin an investigation of relationship between domination, independent transversal domination and equitable domination in graphs.