On the strength of some trees
Let be a graph of order . A numbering of is a labeling that assigns distinct elements of the set to the vertices of , where each edge of is labeled . The strength str of a numbering of is defined by that is, is the maximum edge label of , and the strength str of a graph itself is The strengths and a...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Taylor & Francis Group
2020-01-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1016/j.akcej.2019.06.002 |
| _version_ | 1819061736917958656 |
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| author | Rikio Ichishima Francesc A. Muntaner-Batle Akito Oshima |
| author_facet | Rikio Ichishima Francesc A. Muntaner-Batle Akito Oshima |
| author_sort | Rikio Ichishima |
| collection | DOAJ |
| description | Let be a graph of order . A numbering of is a labeling that assigns distinct elements of the set to the vertices of , where each edge of is labeled . The strength str of a numbering of is defined by that is, is the maximum edge label of , and the strength str of a graph itself is The strengths and are determined for caterpillars and -level complete -ary trees . The strength is also given for graphs obtained by taking the corona of certain graphs and an arbitrary number of isolated vertices. The work of this paper suggests an open problem on the strength of trees. |
| first_indexed | 2024-12-21T14:47:38Z |
| format | Article |
| id | doaj.art-b3bdbaee1d69495280cfb8f6e4ac9f9c |
| institution | Directory Open Access Journal |
| issn | 0972-8600 2543-3474 |
| language | English |
| last_indexed | 2024-12-21T14:47:38Z |
| publishDate | 2020-01-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | AKCE International Journal of Graphs and Combinatorics |
| spelling | doaj.art-b3bdbaee1d69495280cfb8f6e4ac9f9c2022-12-21T18:59:59ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002543-34742020-01-0117148649410.1016/j.akcej.2019.06.0021760662On the strength of some treesRikio Ichishima0Francesc A. Muntaner-Batle1Akito Oshima2Department of Sport and Physical Education, Faculty of Physical Education, Kokushikan UniversityGraph Theory and Applications Research Group, School of Electrical Engineering and Computer Science, Faculty of Engineering and Built Environment, The University of NewcastleGraph Theory and Applications Research Group, School of Electrical Engineering and Computer Science, Faculty of Engineering and Built Environment, The University of NewcastleLet be a graph of order . A numbering of is a labeling that assigns distinct elements of the set to the vertices of , where each edge of is labeled . The strength str of a numbering of is defined by that is, is the maximum edge label of , and the strength str of a graph itself is The strengths and are determined for caterpillars and -level complete -ary trees . The strength is also given for graphs obtained by taking the corona of certain graphs and an arbitrary number of isolated vertices. The work of this paper suggests an open problem on the strength of trees.http://dx.doi.org/10.1016/j.akcej.2019.06.002strengthcaterpillartreegraph labelingcorona |
| spellingShingle | Rikio Ichishima Francesc A. Muntaner-Batle Akito Oshima On the strength of some trees AKCE International Journal of Graphs and Combinatorics strength caterpillar tree graph labeling corona |
| title | On the strength of some trees |
| title_full | On the strength of some trees |
| title_fullStr | On the strength of some trees |
| title_full_unstemmed | On the strength of some trees |
| title_short | On the strength of some trees |
| title_sort | on the strength of some trees |
| topic | strength caterpillar tree graph labeling corona |
| url | http://dx.doi.org/10.1016/j.akcej.2019.06.002 |
| work_keys_str_mv | AT rikioichishima onthestrengthofsometrees AT francescamuntanerbatle onthestrengthofsometrees AT akitooshima onthestrengthofsometrees |