2-Restricted optimal pebbling number of some dendrimers

Document Type : Research Paper

Authors

1 Department of Mathematical Sciences, Yazd University, 89195-741, Yazd, Iran

2 Department of Mathematics, Yazd University, Yazd , Iran

Abstract

This paper studies the 2-restricted optimal pebbling number of certain dendrimer graphs. In graph pebbling, a configuration is a distribution of pebbles on the vertices of a simple connected graph G. A pebbling move removes two pebbles from a vertex and places one on an adjacent vertex. A t-restricted pebbling configuration (tRPC) is an initial placement where no vertex holds more than t pebbles. A configuration is solvable if, for any target vertex v, a sequence of pebbling moves can place at least one pebble on v. The t-restricted optimal pebbling number, denoted πt*(G), is the minimum number of pebbles required for a solvable tRPC on G. We focus on the case t=2 and determine π2*(G) for several classes of dendrimers.

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References

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Journal of Hyperstructures
Volume 15, Issue 1
June 2026
Pages 83-90

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