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.
@article{bwmeta1.element.doi-10_7151_dmgt_1909, author = {Evelyne Flandrin and Hao Li and Antoni Marczyk and Jean-Fran\c cois Sacl\'e and Mariusz Wo\'zniak}, title = {A Note on Neighbor Expanded Sum Distinguishing Index}, journal = {Discussiones Mathematicae Graph Theory}, volume = {37}, year = {2017}, pages = {29-37}, zbl = {1354.05048}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1909} }
Evelyne Flandrin; Hao Li; Antoni Marczyk; Jean-François Saclé; Mariusz Woźniak. A Note on Neighbor Expanded Sum Distinguishing Index. Discussiones Mathematicae Graph Theory, Tome 37 (2017) pp. 29-37. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1909/