Geodesic
A Note on Neighbor Expanded Sum Distinguishing Index
Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 1, pp. 29-37

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A total k-coloring of a graph G is a coloring of vertices and edges of G using colors of the set [k] = 1, . . ., k. These colors can be used to distinguish the vertices of G. There are many possibilities of such a distinction. In this paper, we consider the sum of colors on incident edges and adjacent vertices.
Keywords: general edge coloring, total coloring, neighbor-distinguishing index, neighbor sum distinguishing coloring 
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Flandrin, Evelyne; Li, Hao; Marczyk, Antoni; Saclé, Jean-François; Woźniak, Mariusz. A Note on Neighbor Expanded Sum Distinguishing Index. Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 1, pp. 29-37. http://geodesic.mathdoc.fr/item/DMGT_2017_37_1_a2/