Abstract
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 t 1 , t 2 or t 3 , where $t_{i} = \lceil (1+\sum\sb{j=1}\sp{i}n_{j})/(i+1)\rceil$ and n i is the number of vertices of degree i .
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