Bounds for the pebbling number of product graphs

Q: How can I download an article?

To download an article from SID, first log in to the site, search for the article title, and click on the 'Download Article' option.

Q: How can I download an ISI article?

To download an ISI article on SID, enter the keyword or article title in the search bar, view the relevant results, click on the desired article, and select the 'Download Article' option.

Q: How can I access the SID database?

To access the SID database, visit SID.ir, create an account, and log in to access scientific resources.

Q: Is downloading articles from SID free?

Some articles on SID are available for free, while others require payment. Details are specified on the article's page.

Pleanmani Nopparat; Nupo Nuttawoot; Worawiset Somnuek

مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

Journal Paper

Paper Information

Journal: TRANSACTIONS ON COMBINATORICS Year:2022 | Volume:11 | Issue:4 Page(s): 317-326

Download Full-Text

View:

Download:

Cites:

Information Journal Paper

Title

Bounds for the pebbling number of product graphs

Author(s)

Pleanmani Nopparat | Nupo Nuttawoot | Worawiset Somnuek | Issue Writer Certificate

Keywords

Graph pebbling

Graham's conjecture

product graph

corona

Abstract

Let $G$ be a connected graph. Given a configuration of a fixed number of pebbles on the vertex set of $G$, a pebbling move on $G$ is the process of removing two pebbles from a vertex and adding one pebble on an adjacent vertex. The pebbling number of $G$, denoted by $\pi(G)$, is defined to be the least number of pebbles to guarantee that there is a sequence of pebbling movement that places at least one pebble on each vertex $v$, for any configuration of pebbles on $G$. In this paper, we improve the upper bound of $\pi(G\square H)$ from $2\pi(G)\pi(H)$ to $\left(2-\frac{1}{\min\{\pi(G),\pi(H)\}}\right)\pi(G)\pi(H)$ where $\pi(G)$, $\pi(H)$ and $\pi(G\square H)$ are the pebbling number of graphs $G$, $H$ and the Cartesian product graph $G\square H$, respectively. Moreover, we also discuss such bound for strong product graphs, cross product graphs and coronas.

Multimedia

No record.

Cites

No record.

References

No record.

Cite

Related Journal Papers

No record.

Related Seminar Papers

No record.

Related Plans