On a Total Version of 1-2-3 Conjecture - Baudon Olivier; Hocquard Hervé; Marczyk Antoni; Pilśniak Monika; Przybyło Jakub; Woźniak Mariusz (Discussiones Mathematicae Graph Theory, 2020)
A total k-coloring of a graph G is a coloring of vertices and edges of G using colors of the set {1, . . . , k}. These colors can be used to distinguish adjacent vertices of G. There are many possibilities of such a distinction. In this paper, we focus on the one by the full sum of colors of a vertex, i.e., the sum of the color of the vertex, the colors on its incident edges and the colors on its adjacent vertices.