Graham's Pebbling Conjecture Holds for the Product of a Graph and a Sufficiently Large Complete Graph
| Autor: | Nopparat Pleanmani |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Theory and Applications of Graphs, Vol 7 (2020) |
| Druh dokumentu: | article |
| ISSN: | 2470-9859 |
| DOI: | 10.20429/tag.2020.070101 |
| Popis: | For connected graphs $G$ and $H$, Graham conjectured that $\pi(G\square H)\leq\pi(G)\pi(H)$ where $\pi(G), \pi(H)$, and $\pi(G\square H)$ are the pebbling numbers of $G$, $H$, and the Cartesian product $G\square H$, respectively. In this paper, we show that the inequality holds when $H$ is a complete graph of sufficiently large order in terms of graph parameters of $G$. |
| Databáze: | Directory of Open Access Journals |
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