The restricted edge pebbling distribution is a distribution of pebbles on the edges of G is the placement of pebbles on the edges with the restriction that only an even number of pebbles should be placed on the edges with labels $0$. Given an SDC labeling of G, the restricted SDC edge cover pebbling number of a graph G, ψEC(G), is the least positive integer m for which any restricted edge pebbling distribution of m pebbles such that at the end there are no pebbles on the edges having label $0$ will allow the shifting of a pebble simultaneously to all edges with label $1$ using a sequence of restricted edge pebbling moves. We compute the restricted SDC edge cover pebbling number for some graphs
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Lourdusamy et al. (2024) studied this question.
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