# $t$-Pebbling in $k$-connected diameter two graphs

## TL;DR

This paper investigates the $t$-pebbling number in diameter two graphs, focusing on how connectivity influences resource transportation modeled by pebbling moves.

## Contribution

It extends the study of pebbling numbers by analyzing the $t$-pebbling number in diameter two graphs with respect to their connectivity.

## Key findings

- Characterizes $t$-pebbling numbers in diameter two graphs.
- Highlights the role of connectivity in pebbling resource distribution.
- Provides bounds or formulas for $t$-pebbling numbers based on graph properties.

## Abstract

Graph pebbling models the transportation of consumable resources. As two pebbles move across an edge, one reaches its destination while the other is consumed. The $t$-pebbling number is the smallest integer $m$ so that any initially distributed supply of $m$ pebbles can place $t$ pebbles on any target vertex via pebbling moves. The 1-pebbling number of diameter two graphs is well-studied. Here we investigate the $t$-pebbling number of diameter two graphs under the lense of connectivity.