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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 = (1 + i j=1 n j )/(i + 1) and n i is the number of vertices of degree i.doi:10.5614/ejgta.2018.6.2.5 fatcat:vjoaa5eswvavdk3totvja5jvrm