Total vertex irregularity strength of trees with maximum degree five
In 2010, Nurdin, Baskoro, Salman and Gaos conjectured that the total vertex irregularity strength of any tree T is determined only by the number of vertices of degrees 1, 2 and 3 in T. This paper will confirm this conjecture by considering all trees with maximum degree five. Furthermore, we also cha...
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| Main Authors: | , , |
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| Format: | EJournal Article |
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GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB,
2018-10-10.
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| Online Access: | Get Fulltext Get Fulltext |
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| Summary: | In 2010, Nurdin, Baskoro, Salman and Gaos conjectured that the total vertex irregularity strength of any tree T is determined only by the number of vertices of degrees 1, 2 and 3 in T. This paper will confirm this conjecture by considering all trees with maximum degree five. Furthermore, we also characterize all such trees having the total vertex irregularity strength either t1, t2 or t3, where $t_{i} = \lceil (1+\sum\sb{j=1}\sp{i}n_{j})/(i+1)\rceil$ and ni is the number of vertices of degree i. |
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| Item Description: | https://www.ejgta.org/index.php/ejgta/article/view/415 |