Optimal L(3,2,1)-labeling of trees
| Autor: | Xiaoling Zhang |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | AKCE International Journal of Graphs and Combinatorics, Vol 21, Iss 3, Pp 310-314 (2024) |
| Druh dokumentu: | article |
| ISSN: | 09728600 2543-3474 0972-8600 |
| DOI: | 10.1080/09728600.2024.2358691 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
| Externí odkaz: |
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