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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Pranaya D. M. Taihuttu
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Pattimura, Jalan Ir. M. Putuhena, Kampus Unpatti Poka Ambon, Indonesia
Electrical & Electronics Engineering

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Complete bipartite graph is a totally irregular total graph Meilin I. Tilukay; Pranaya D. M. Taihuttu; A. N. M. Salman; Francis Y. Rumlawang; Zeth A. Leleury
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 2 (2021): 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.2021.9.2.11

Abstract

A graph G is called a totally irregular total k-graph if it has a totally irregular total k-labeling λ : V ∪ E→ 1, 2, ... , k, that is a total labeling such that for any pair of different vertices x and y of G, their weights wt(x) and wt(y) are distinct, and for any pair of different edges e and f of G, their weights wt(e) and wt(f) are distinct. The minimum value k under labeling λ is called the total irregularity strength of G, denoted by ts(G). For special cases of a complete bipartite graph Km, n, the ts(K1, n) and the ts(Kn, n) are already determined for any positive integer n. Completing the results, this paper deals with the total irregularity strength of complete bipartite graph Km, n for any positive integer m and n.
Co-Authors A. N. M. Salman Francis Y. Rumlawang Meilin Imelda Tilukay Zeth A. Leleury