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arXiv · 2305.04463

Non-split Domination Cover Pebbling Number for Some Class of Middle Graphs

A. Lourdusamy·I. Dhivviyanandam·Lian Mathew
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Abstract

Let $G$ be a connected graph. A pebbling move is defined as taking two pebbles from one vertex and placing one pebble to an adjacent vertex and throwing away the other pebble. The non-split domination cover pebbling number, $\psi_{ns}(G)$, of a graph $G$ is the minimum of pebbles that must be placed on $V(G)$ such that after a sequence of pebbling moves, the set of vertices with a pebble forms a non-split dominating set of $G$, regardless of the initial configuration of pebbles. We discuss some basic results, NP-completeness of non-split domination number, and determine $\psi_{ns}$ for some families of Middle graphs.

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A. Lourdusamy, I. Dhivviyanandam, Lian Mathew. 2023-05-08. Non-split Domination Cover Pebbling Number for Some Class of Middle Graphs. https://arxiv.org/abs/2305.04463

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