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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Rinovia Simanjuntak
Combinatorial Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesha 10 Bandung, Indonesia
Electrical & Electronics Engineering

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Total vertex irregularity strength for trees with many vertices of degree two Rinovia Simanjuntak; Susilawati Susilawati; Edy Tri Baskoro
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 8, No 2 (2020): 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.2020.8.2.17

Abstract

For a simple graph G = (V,E), a mapping φ : V ∪ E → {1,2,...,k} is defined as a vertex irregular total k-labeling of G if for every two different vertices x and y, wt(x) ≠ wt(y), where wt(x) = φ(x)+ Σ????xy∈E(G) φ(xy). The minimum k for which the graph G has a vertex irregular total k-labeling is called the total vertex irregularity strength of G. In this paper, we provide three possible values of total vertex irregularity strength for trees with many vertices of degree two. For each of the possible values, sufficient conditions for trees with corresponding total vertex irregularity strength are presented.
Co-Authors Edy Tri Baskoro Susilawati, Susilawati