Herscovici Conjecture on Pebbling
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866913768144896000 |
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| author | Dhivviyanandam, I. Lourdusamy, A. Iammal, S. Kither Rani, K. Christy |
| author_facet | Dhivviyanandam, I. Lourdusamy, A. Iammal, S. Kither Rani, K. Christy |
| contents | Consider a configuration of pebbles on the vertices of a connected graph. A pebbling move is to remove two pebbles from a vertex and to place one pebble at the neighbouring vertex of the vertex from which the pebbles are removed.
For a positive integer $t$, with every configuration of $π_t(G)$(least positive integer) pebbles, if we can transfer $t$ pebbles to any target through a number of pebbling moves then $π_t(G)$ is called the $t$-pebbling number of $G$.
We discuss the computation of the $t$-pebbling number, the $2t-$ pebbling property and Herscovici conjecture considering total graphs.
\bigskip \noindent Keywords: pebbling moves, $t$- pebbling number, $2t$-pebbling property, Herscovici conjecture, total graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_23802 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Herscovici Conjecture on Pebbling Dhivviyanandam, I. Lourdusamy, A. Iammal, S. Kither Rani, K. Christy Combinatorics 05C12, 05C25, 05C38, 05C76 F.2.2; G.2.1 Consider a configuration of pebbles on the vertices of a connected graph. A pebbling move is to remove two pebbles from a vertex and to place one pebble at the neighbouring vertex of the vertex from which the pebbles are removed. For a positive integer $t$, with every configuration of $π_t(G)$(least positive integer) pebbles, if we can transfer $t$ pebbles to any target through a number of pebbling moves then $π_t(G)$ is called the $t$-pebbling number of $G$. We discuss the computation of the $t$-pebbling number, the $2t-$ pebbling property and Herscovici conjecture considering total graphs. \bigskip \noindent Keywords: pebbling moves, $t$- pebbling number, $2t$-pebbling property, Herscovici conjecture, total graphs. |
| title | Herscovici Conjecture on Pebbling |
| topic | Combinatorics 05C12, 05C25, 05C38, 05C76 F.2.2; G.2.1 |
| url | https://arxiv.org/abs/2503.23802 |