On a total version of 1-2-3 Conjecture
Olivier Baudon, Hervé Hocquard, Antoni Marczyk, Monika Pilśniak, Jakub Przybyło, Mariusz Woźniak · Discussiones Mathematicae Graph Theory · 2019
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.