## Total Vertex Irregularity Strength of Disjoint Union of Helm Graphs

 Ali Ahmad College of Computer Science and Information Systems Jazan University, Jazan Kingdom of Saudi Arabia E.T. Baskoro Combinatorial Mathematics Research Group Faculty of Mathematics and Natural Sciences Institut Teknologi Bandung, Indonesia M. Imran Center for Advanced Mathematics and Physics (CAMP) National University of Science and Technology (NUST) H-12 Sector, Islamabad, Pakistan

## 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.

Keywords: vertex irregular total k-labeling, Helm graphs, total vertex irregularity strength

2010 Mathematics Subject Classification: 05C78.

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