Mathematics

On sum edge-colorings of complete tripartite graphs

G. V. Mikaelyan

Yerevan State University, Faculty of Informatics and Applied Mathematics

Abstract: A proper edge-coloring of a graph is called a sum edge-coloring if it minimizes the total sum of colors on all the edges of the graph. The aforementioned minimal sum is called the edge-chromatic sum of the graph, and the minimal number of colors needed for a sum edge-coloring is called the edge-strength of the graph. In this paper, upper bounds on the values of the edge-chromatic sums of some complete tripartite graphs are given, while for some other complete tripartite graphs, the exact values of both parameters are obtained.

Keywords: edge-coloring, sum edge-coloring, edge-strength

MSC: 05C15

Received: 05.10.2025
Revised: 18.11.2025
Accepted: 25.11.2025

Language: English

DOI: 10.46991/PYSU:A.2024.59.3.069