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arXiv · 2406.02259

Restricted SDC Edge Cover Pebbling Number

A. Lourdusamy·F. Joy Beaula·F. Patrick·I. Dhivviyanandam
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Abstract

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 $G$, $\psi_{EC}(G)$, 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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A. Lourdusamy, F. Joy Beaula, F. Patrick, I. Dhivviyanandam. 2024-06-04. Restricted SDC Edge Cover Pebbling Number. https://arxiv.org/abs/2406.02259

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