Total vertex irregularity strength of disjoint union of Helm graphs

Ali Ahmad; E.T. Baskoro; M. Imran

Discussiones Mathematicae Graph Theory (2012)

  • Volume: 32, Issue: 3, page 427-434
  • ISSN: 2083-5892

Abstract

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A total vertex irregular k-labeling φ of a graph G is a labeling of the vertices and edges of G with labels from the set {1,2,...,k} in such a way that for any two different vertices x and y their weights wt(x) and wt(y) are distinct. Here, the weight of a vertex x in G is the sum of the label of x and the labels of all edges incident with the vertex x. The minimum k for which the graph G has a vertex irregular total k-labeling is called the total vertex irregularity strength of G. We have determined an exact value of the total vertex irregularity strength of disjoint union of Helm graphs.

How to cite

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Ali Ahmad, E.T. Baskoro, and M. Imran. "Total vertex irregularity strength of disjoint union of Helm graphs." Discussiones Mathematicae Graph Theory 32.3 (2012): 427-434. <http://eudml.org/doc/270908>.

@article{AliAhmad2012,
abstract = {A total vertex irregular k-labeling φ of a graph G is a labeling of the vertices and edges of G with labels from the set \{1,2,...,k\} in such a way that for any two different vertices x and y their weights wt(x) and wt(y) are distinct. Here, the weight of a vertex x in G is the sum of the label of x and the labels of all edges incident with the vertex x. The minimum k for which the graph G has a vertex irregular total k-labeling is called the total vertex irregularity strength of G. We have determined an exact value of the total vertex irregularity strength of disjoint union of Helm graphs.},
author = {Ali Ahmad, E.T. Baskoro, M. Imran},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {vertex irregular total k-labeling; Helm graphs; total vertex irregularity strength; vertex irregular total -labeling; total vertex irregularity},
language = {eng},
number = {3},
pages = {427-434},
title = {Total vertex irregularity strength of disjoint union of Helm graphs},
url = {http://eudml.org/doc/270908},
volume = {32},
year = {2012},
}

TY - JOUR
AU - Ali Ahmad
AU - E.T. Baskoro
AU - M. Imran
TI - Total vertex irregularity strength of disjoint union of Helm graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2012
VL - 32
IS - 3
SP - 427
EP - 434
AB - A total vertex irregular k-labeling φ of a graph G is a labeling of the vertices and edges of G with labels from the set {1,2,...,k} in such a way that for any two different vertices x and y their weights wt(x) and wt(y) are distinct. Here, the weight of a vertex x in G is the sum of the label of x and the labels of all edges incident with the vertex x. The minimum k for which the graph G has a vertex irregular total k-labeling is called the total vertex irregularity strength of G. We have determined an exact value of the total vertex irregularity strength of disjoint union of Helm graphs.
LA - eng
KW - vertex irregular total k-labeling; Helm graphs; total vertex irregularity strength; vertex irregular total -labeling; total vertex irregularity
UR - http://eudml.org/doc/270908
ER -

References

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