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All Journal Electronic Journal of Graph Theory and Applications (EJGTA) Jurnal Fourier Jambura Journal of Mathematics Jurnal Matematika UNAND Community Development Journal: Jurnal Pengabdian Masyarakat
Susilawati, S.
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Humanities Computer Science & IT Economics, Econometrics & Finance Education Electrical & Electronics Engineering Health Professions Mathematics Public Health

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Journal : Electronic Journal of Graph Theory and Applications (EJGTA)

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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.
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 Abdullah Abdullah Asmadi M. Noer Edy Tri Baskoro Efni Agustiarini, Efni Lenny Anwar Maria Erna Nasfianti, Iis Nasution, Dina Khairani Nasution, Dinda Khairani Putri Adita Wulandari Rinovia Simanjuntak Rinovia Simanjuntak