# DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

# IMPACT FACTOR 2018: 0.741

SCImago Journal Rank (SJR) 2018: 0.763

Rejection Rate (2017-2018): c. 84%

# Discussiones Mathematicae Graph Theory

Article in press

Authors:

O. Baudon, H. Hocquard, A. Marczyk, M. Pilśniak, J. Przybyło, M. Woźniak

Title:

On a total version of 1-2-3 Conjecture

Source:

Discussiones Mathematicae Graph Theory

Received: 2018-06-12, Revised: 2019-04-23, Accepted: 2019-04-23, https://doi.org/10.7151/dmgt.2223

Abstract:

A total $k$-coloring of a graph $G$ is a coloring of vertices and edges of $G$ using colors of the set $\{1,\ldots,k\}$. 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.<br>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.

Keywords:

neighbor sum distinguishing total coloring, general edge coloring, total coloring, neighbor-distinguishing index, neighbor full sum distinguishing total $k$-coloring