The optimal pebbling of spindle graphs
Given a distribution of pebbles on the vertices of a connected graph G, a pebbling move on G consists of taking two pebbles off one vertex and placing one on an adjacent vertex. The optimal pebbling number of G, denoted by πopt(G), is the smallest number m such that for some distribution of m pebble...
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| Fformat: | Erthygl |
| Iaith: | English |
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De Gruyter
2019-11-01
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| Cyfres: | Open Mathematics |
| Pynciau: | |
| Mynediad Ar-lein: | https://doi.org/10.1515/math-2019-0094 |
| _version_ | 1831582292496089088 |
|---|---|
| author | Gao Ze-Tu Yin Jian-Hua |
| author_facet | Gao Ze-Tu Yin Jian-Hua |
| author_sort | Gao Ze-Tu |
| collection | DOAJ |
| description | Given a distribution of pebbles on the vertices of a connected graph G, a pebbling move on G consists of taking two pebbles off one vertex and placing one on an adjacent vertex. The optimal pebbling number of G, denoted by πopt(G), is the smallest number m such that for some distribution of m pebbles on G, one pebble can be moved to any vertex of G by a sequence of pebbling moves. Let Pk be the path on k vertices. Snevily defined the n–k spindle graph as follows: take n copies of Pk and two extra vertices x and y, and then join the left endpoint (respectively, the right endpoint) of each Pk to x (respectively, y), the resulting graph is denoted by S(n, k), and called the n–k spindle graph. In this paper, we determine the optimal pebbling number for spindle graphs. |
| first_indexed | 2024-12-17T20:21:45Z |
| format | Article |
| id | doaj.art-c1cb4e2904334013bc8889cfe8a7c008 |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-12-17T20:21:45Z |
| publishDate | 2019-11-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-c1cb4e2904334013bc8889cfe8a7c0082022-12-21T21:33:55ZengDe GruyterOpen Mathematics2391-54552019-11-0117158258710.1515/math-2019-0094math-2019-0094The optimal pebbling of spindle graphsGao Ze-Tu0Yin Jian-Hua1School of Science, Hainan University, Haikou, 570228, P.R. ChinaSchool of Science, Hainan University, Haikou, 570228, P.R. ChinaGiven a distribution of pebbles on the vertices of a connected graph G, a pebbling move on G consists of taking two pebbles off one vertex and placing one on an adjacent vertex. The optimal pebbling number of G, denoted by πopt(G), is the smallest number m such that for some distribution of m pebbles on G, one pebble can be moved to any vertex of G by a sequence of pebbling moves. Let Pk be the path on k vertices. Snevily defined the n–k spindle graph as follows: take n copies of Pk and two extra vertices x and y, and then join the left endpoint (respectively, the right endpoint) of each Pk to x (respectively, y), the resulting graph is denoted by S(n, k), and called the n–k spindle graph. In this paper, we determine the optimal pebbling number for spindle graphs.https://doi.org/10.1515/math-2019-0094pebblingoptimal pebblingspindle graph05c35 |
| spellingShingle | Gao Ze-Tu Yin Jian-Hua The optimal pebbling of spindle graphs Open Mathematics pebbling optimal pebbling spindle graph 05c35 |
| title | The optimal pebbling of spindle graphs |
| title_full | The optimal pebbling of spindle graphs |
| title_fullStr | The optimal pebbling of spindle graphs |
| title_full_unstemmed | The optimal pebbling of spindle graphs |
| title_short | The optimal pebbling of spindle graphs |
| title_sort | optimal pebbling of spindle graphs |
| topic | pebbling optimal pebbling spindle graph 05c35 |
| url | https://doi.org/10.1515/math-2019-0094 |
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