Geodesic
Total vertex irregularity strength of disjoint union of Helm graphs
Discussiones Mathematicae. Graph Theory, Tome 32 (2012) no. 3, pp. 427-434

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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.
Keywords: vertex irregular total k-labeling, Helm graphs, total vertex irregularity strength 
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Ahmad, Ali; Baskoro, E.; Imran, M. Total vertex irregularity strength of disjoint union of Helm graphs. Discussiones Mathematicae. Graph Theory, Tome 32 (2012) no. 3, pp. 427-434. http://geodesic.mathdoc.fr/item/DMGT_2012_32_3_a3/