On the Secure Vertex Cover Pebbling Number
Combinatorics
2022-12-22 v1
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 G is the minimum number m so that every distribution of m pebbles can reach some secure vertex cover of G 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 r- partite graphs, paths, Friendship graphs, and wheel graphs.
Keywords
Cite
@article{arxiv.2212.10850,
title = {On the Secure Vertex Cover Pebbling Number},
author = {Glenn H Hurlbert and Lian Mathew and Jasintha Quadras and S Sarah Surya},
journal= {arXiv preprint arXiv:2212.10850},
year = {2022}
}
Comments
19 pages, 3 figures