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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Main Authors:	Ibrahim,Muhammad, Khan,S., Asim,Muhammad Ahsan, Waseem,Muhammad
Language:	English
Published:	Universidad Católica del Norte, Departamento de Matemáticas 2021
Subjects:	Total edge irregularity strength Total vertex irregularity strength Total irregularity strength Plane graph Crossed prism graph Necklace graph Goldberg snark graph
Online Access:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000400905
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spelling	oai:scielo:S0716-091720210004009052021-08-12Total irregularity strength of some cubic graphsIbrahim,MuhammadKhan,S.Asim,Muhammad AhsanWaseem,Muhammad Total edge irregularity strength Total vertex irregularity strength Total irregularity strength Plane graph Crossed prism graph Necklace graph Goldberg snark graph 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.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.40 n.4 20212021-01-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000400905en10.22199/issn.0717-6279-3715
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Total edge irregularity strength Total vertex irregularity strength Total irregularity strength Plane graph Crossed prism graph Necklace graph Goldberg snark graph
spellingShingle	Total edge irregularity strength Total vertex irregularity strength Total irregularity strength Plane graph Crossed prism graph Necklace graph Goldberg snark graph Ibrahim,Muhammad Khan,S. Asim,Muhammad Ahsan Waseem,Muhammad Total irregularity strength of some cubic graphs
description	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.
author	Ibrahim,Muhammad Khan,S. Asim,Muhammad Ahsan Waseem,Muhammad
author_facet	Ibrahim,Muhammad Khan,S. Asim,Muhammad Ahsan Waseem,Muhammad
author_sort	Ibrahim,Muhammad
title	Total irregularity strength of some cubic graphs
title_short	Total irregularity strength of some cubic graphs
title_full	Total irregularity strength of some cubic graphs
title_fullStr	Total irregularity strength of some cubic graphs
title_full_unstemmed	Total irregularity strength of some cubic graphs
title_sort	total irregularity strength of some cubic graphs
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2021
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000400905
work_keys_str_mv	AT ibrahimmuhammad totalirregularitystrengthofsomecubicgraphs AT khans totalirregularitystrengthofsomecubicgraphs AT asimmuhammadahsan totalirregularitystrengthofsomecubicgraphs AT waseemmuhammad totalirregularitystrengthofsomecubicgraphs
_version_	1718439910292062208

Total irregularity strength of some cubic graphs

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