Further results on the total vertex irregularity strength of trees

Susanto, Faisal (Institut Teknologi Bandung)
Simanjuntak, Rinovia (Institut Teknologi Bandung)
Baskoro, Edy Tri (Institut Teknologi Bandung)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 13, No 1 (2025): Electronic Journal of Graph Theory and Applications

We investigate the total vertex irregularity strength of trees with specific characteristics. Initially, we categorize trees into three distinct groups: types A, B, and C. Subsequently, we calculate tvs(T) for all type A trees T where the maximum degree is at least three. Additionally, we provide the value of tvs(T) whenever T is a tree of types B or C with maximum degree at least three and large number of exterior vertices. Finally, we propose a conjecture related to tvs(T) where T is a non-path tree of types B or C with few exterior vertices.