Optimal L(3,2,1)-labeling of trees
Given a graph G, an [Formula: see text]-labeling of G is an assignment f of non-negative integers (labels) to the vertices of G such that [Formula: see text] if [Formula: see text] (i = 1, 2, 3). For a non-negative integer k, a k-[Formula: see text]-labeling is an [Formula: see text]-labeling such t...
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Taylor & Francis Group
2024-09-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
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| Online Access: | https://www.tandfonline.com/doi/10.1080/09728600.2024.2358691 |
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| author | Xiaoling Zhang |
| author_facet | Xiaoling Zhang |
| author_sort | Xiaoling Zhang |
| collection | DOAJ |
| description | Given a graph G, an [Formula: see text]-labeling of G is an assignment f of non-negative integers (labels) to the vertices of G such that [Formula: see text] if [Formula: see text] (i = 1, 2, 3). For a non-negative integer k, a k-[Formula: see text]-labeling is an [Formula: see text]-labeling such that no label is greater than k. The [Formula: see text]-labeling number of G, denoted by [Formula: see text], is the smallest number k such that G has a k-[Formula: see text]-labeling. Chia proved that the [Formula: see text]-labeling number of a tree T with maximum degree Δ can have one of three values: [Formula: see text] and [Formula: see text]. This paper gives some sufficient conditions for [Formula: see text] and [Formula: see text], respectively. As a result, the [Formula: see text]-labeling numbers of complete m-ary trees, spiders and banana trees are completely determined. |
| format | Article |
| id | doaj-art-5c83ea2ba5e546f8b7122bb2480903d0 |
| institution | OA Journals |
| issn | 0972-8600 2543-3474 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | AKCE International Journal of Graphs and Combinatorics |
| spelling | doaj-art-5c83ea2ba5e546f8b7122bb2480903d02025-08-20T02:19:04ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002543-34742024-09-0121331031410.1080/09728600.2024.2358691Optimal L(3,2,1)-labeling of treesXiaoling Zhang0Teachers College, Jimei University, Xiamen, Fujian, ChinaGiven a graph G, an [Formula: see text]-labeling of G is an assignment f of non-negative integers (labels) to the vertices of G such that [Formula: see text] if [Formula: see text] (i = 1, 2, 3). For a non-negative integer k, a k-[Formula: see text]-labeling is an [Formula: see text]-labeling such that no label is greater than k. The [Formula: see text]-labeling number of G, denoted by [Formula: see text], is the smallest number k such that G has a k-[Formula: see text]-labeling. Chia proved that the [Formula: see text]-labeling number of a tree T with maximum degree Δ can have one of three values: [Formula: see text] and [Formula: see text]. This paper gives some sufficient conditions for [Formula: see text] and [Formula: see text], respectively. As a result, the [Formula: see text]-labeling numbers of complete m-ary trees, spiders and banana trees are completely determined.https://www.tandfonline.com/doi/10.1080/09728600.2024.2358691Channel assignment-labelingtrees05C7805C15 |
| spellingShingle | Xiaoling Zhang Optimal L(3,2,1)-labeling of trees AKCE International Journal of Graphs and Combinatorics Channel assignment -labeling trees 05C78 05C15 |
| title | Optimal L(3,2,1)-labeling of trees |
| title_full | Optimal L(3,2,1)-labeling of trees |
| title_fullStr | Optimal L(3,2,1)-labeling of trees |
| title_full_unstemmed | Optimal L(3,2,1)-labeling of trees |
| title_short | Optimal L(3,2,1)-labeling of trees |
| title_sort | optimal l 3 2 1 labeling of trees |
| topic | Channel assignment -labeling trees 05C78 05C15 |
| url | https://www.tandfonline.com/doi/10.1080/09728600.2024.2358691 |
| work_keys_str_mv | AT xiaolingzhang optimall321labelingoftrees |