# Total vertex irregularity strength of disjoint union of Helm graphs

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

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## 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>.

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.},
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 - 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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