Geodesic
Total vertex irregularity strength of convex polytope graphs
Acta mathematica Universitatis Comenianae, Tome 82 (2013) no. 1, pp. 29-38 
A. Arshad; O. Al-Mushayt; M. K. Siddiqui; A. Arshad; O. Al-Mushayt; M. K. Siddiqui. Total vertex irregularity strength of convex polytope graphs. Acta mathematica Universitatis Comenianae, Tome 82 (2013) no. 1, pp. 29-38. http://geodesic.mathdoc.fr/item/AMUC_2013_82_1_a3/
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     author = {A. Arshad and O. Al-Mushayt and M. K. Siddiqui and A. Arshad and O. Al-Mushayt and M. K. Siddiqui},
     title = { Total vertex irregularity strength of convex polytope graphs},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {29--38},
     year = {2013},
     volume = {82},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2013_82_1_a3/}
}
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Voir la notice de l'article provenant de la source Comenius University

A total vertex irregular k-labeling j 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 some convex polytope graphs.