Total irregularity strength of some cubic graphs
Abstract Let G = (V;E) be a graph. A total labeling ψ : V ⋃ E → {1, 2, ....k} is called totally irregular total k-labeling of G if every two distinct vertices u and v in V (G) satisfy wt(u) ≠wt(v); and every two distinct edges u 1 u 2 and v 1 v 2 in E(G) sa...
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| Autores principales: | , , , |
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| Lenguaje: | English |
| Publicado: |
Universidad Católica del Norte, Departamento de Matemáticas
2021
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| Materias: | |
| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000400905 |
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| Sumario: | Abstract Let G = (V;E) be a graph. A total labeling ψ : V ⋃ E → {1, 2, ....k} is called totally irregular total k-labeling of G if every two distinct vertices u and v in V (G) satisfy wt(u) ≠wt(v); and every two distinct edges u 1 u 2 and v 1 v 2 in E(G) satisfy wt(u 1 u 2 ) ≠ wt(v 1 v 2 ); where wt(u) = ψ (u) + ∑ uv∊E(G) ψ(uv) and wt(u 1 u 2 ) = ψ(u 1 ) + ψ(u 1 u 2 ) + ψ(u 2 ): The minimum k for which a graph G has a totally irregular total k-labeling is called the total irregularity strength of G, denoted by ts(G): In this paper, we determine the exact value of the total irregularity strength of cubic graphs. |
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