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Rinovia Simanjuntak
Combinatorial Mathematics Research Group Faculty of Mathematics and Natural Sciences Institut Teknologi Bandung, Indonesia
Electrical & Electronics Engineering

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Total vertex irregularity strength of trees with maximum degree five S. Susilawati; Edy Tri Baskoro; Rinovia Simanjuntak
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 6, No 2 (2018): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2018.6.2.5

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 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.
Co-Authors Edy Tri Baskoro Susilawati, S.