On the secure vertex cover pebbling number

Abstract

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.