Total vertex irregularity strength of trees with maximum degree five

S Susilawati, Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha 10 Bandung, Edy Tri Baskoro, Rinovia Simanjuntak
2018 Electronic Journal of Graph Theory and Applications  
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