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- W4386113885 abstract "Let $G=(V,E)$ be a simple graph. A function $f:Vrightarrow mathbb{N}cup {0}$ is called a configuration of pebbles on the vertices of $G$ and the weight of $f$ is $w(f)=sum_{uin V}f(u)$ which is just the total number of pebbles assigned to vertices. A pebbling step from a vertex $u$ to one of its neighbors $v$ reduces $f(u)$ by two and increases $f(v)$ by one. A pebbling configuration $f$ is said to be solvable if for every vertex $ v $, there exists a sequence (possibly empty) of pebbling moves that results in a pebble on $v$. A pebbling configuration $f$ is a $t$-restricted pebbling configuration (abbreviated $t$RPC) if $f(v)leq t$ for all $vin V$. The $t$-restricted optimal pebbling number $pi_t^*(G)$ is the minimum weight of a solvable $t$RPC on $G$. Chellali et.al. [Discrete Appl. Math. 221 (2017) 46-53] characterized connected graphs $G$ having small $2$-restricted optimal pebbling numbers and characterization of graphs $G$ with $pi_2^*(G)=5$ stated as an open problem. In this paper, we solve this problem. We improve the upper bound of the $2$-restricted optimal pebbling number of trees of order $n$. Also, we study $2$-restricted optimal pebbling number of some grid graphs, corona and neighborhood corona of two specific graphs." @default.
- W4386113885 created "2023-08-24" @default.
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- W4386113885 date "2023-08-18" @default.
- W4386113885 modified "2023-09-27" @default.
- W4386113885 title "More on the $2$-restricted optimal pebbling number" @default.
- W4386113885 doi "https://doi.org/10.48550/arxiv.2308.11028" @default.
- W4386113885 hasPublicationYear "2023" @default.
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