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 characterize all such trees having the total vertex irregularity strength either t(1), t(2) or t(3), where t(i) = inverted right perpendicular(1 + Sigma(i)(j=1) n(j))/(i + 1)inverted left perpendicular and n(i) is the number of vertices of degree i.