On a total version of 1,2,3 Conjecture

Hervé Hocquard (1) , Olivier Baudon (1) , Antoni Marczyk (2) , Monika Pilśniak (2) , Jakub Przybyło (2) , Mariusz Woźniak (2)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 AGH UST - AGH University of Science and Technology [Krakow, PL]

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. This way of distinguishing vertices has similar properties to the method when we only use incident edge colors and to the corresponding 1-2-3 Conjecture .

Mots clés: neighbor sum distinguishing total coloring; general edge; coloring; total coloring; neighbor-distinguishing index; neighbor full; sum distinguishing total k-coloring

Domaines: Mathématique discrète [cs.DM]

Hervé Hocquard, Olivier Baudon, Antoni Marczyk, Monika Pilśniak, Jakub Przybyło, et al.. On a total version of 1,2,3 Conjecture. 2018. ⟨hal-01754080⟩