On subset labelings of trees
AbstractFor a nontrivial graph G, a subset labeling of G is a labeling of the vertices of G with nonempty subsets of the set [Formula: see text] for a positive integer r such that two vertices of G have disjoint labels if and only if the vertices are adjacent. The subset index [Formula: see text] of...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Taylor & Francis Group
2024-01-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
| Subjects: | |
| Online Access: | https://www.tandfonline.com/doi/10.1080/09728600.2023.2254562 |
| _version_ | 1797244257799503872 |
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| author | Gary Chartrand Ebrahim Salehi Ping Zhang |
| author_facet | Gary Chartrand Ebrahim Salehi Ping Zhang |
| author_sort | Gary Chartrand |
| collection | DOAJ |
| description | AbstractFor a nontrivial graph G, a subset labeling of G is a labeling of the vertices of G with nonempty subsets of the set [Formula: see text] for a positive integer r such that two vertices of G have disjoint labels if and only if the vertices are adjacent. The subset index [Formula: see text] of G is the minimum positive integer r for which G has such a subset labeling from the set [Formula: see text]. If T is a tree of diameter d, then [Formula: see text]. It is shown that there are several classes of trees T of diameter d such that [Formula: see text] and for every pair a, b of integers with [Formula: see text], there is a tree T of diameter d such that [Formula: see text] and [Formula: see text]. Sharp bounds are established for the subset indices of the starlike trees [Formula: see text] obtained by subdividing each edge of the star [Formula: see text]a total of r times. Other results and open questions are also presented on subset indices of trees. |
| first_indexed | 2024-03-12T01:26:06Z |
| format | Article |
| id | doaj.art-3c13443447914d6b859dbe51d9bc8704 |
| institution | Directory Open Access Journal |
| issn | 0972-8600 2543-3474 |
| language | English |
| last_indexed | 2024-04-24T19:08:08Z |
| publishDate | 2024-01-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | AKCE International Journal of Graphs and Combinatorics |
| spelling | doaj.art-3c13443447914d6b859dbe51d9bc87042024-03-26T14:03:26ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002543-34742024-01-01211849010.1080/09728600.2023.2254562On subset labelings of treesGary Chartrand0Ebrahim Salehi1Ping Zhang2Department of Mathematics, Western Michigan University, Kalamazoo, MI, USADepartment of Mathematical Sciences, University of Nevada Las Vegas, Las Vegas, NV, USADepartment of Mathematics, Western Michigan University, Kalamazoo, MI, USAAbstractFor a nontrivial graph G, a subset labeling of G is a labeling of the vertices of G with nonempty subsets of the set [Formula: see text] for a positive integer r such that two vertices of G have disjoint labels if and only if the vertices are adjacent. The subset index [Formula: see text] of G is the minimum positive integer r for which G has such a subset labeling from the set [Formula: see text]. If T is a tree of diameter d, then [Formula: see text]. It is shown that there are several classes of trees T of diameter d such that [Formula: see text] and for every pair a, b of integers with [Formula: see text], there is a tree T of diameter d such that [Formula: see text] and [Formula: see text]. Sharp bounds are established for the subset indices of the starlike trees [Formula: see text] obtained by subdividing each edge of the star [Formula: see text]a total of r times. Other results and open questions are also presented on subset indices of trees.https://www.tandfonline.com/doi/10.1080/09728600.2023.2254562Subset labelingsubset indextree05C0505C7505C78 |
| spellingShingle | Gary Chartrand Ebrahim Salehi Ping Zhang On subset labelings of trees AKCE International Journal of Graphs and Combinatorics Subset labeling subset index tree 05C05 05C75 05C78 |
| title | On subset labelings of trees |
| title_full | On subset labelings of trees |
| title_fullStr | On subset labelings of trees |
| title_full_unstemmed | On subset labelings of trees |
| title_short | On subset labelings of trees |
| title_sort | on subset labelings of trees |
| topic | Subset labeling subset index tree 05C05 05C75 05C78 |
| url | https://www.tandfonline.com/doi/10.1080/09728600.2023.2254562 |
| work_keys_str_mv | AT garychartrand onsubsetlabelingsoftrees AT ebrahimsalehi onsubsetlabelingsoftrees AT pingzhang onsubsetlabelingsoftrees |