*Article* **The** *t***-Graphs over Finitely Generated Groups and the Minkowski Metric**

**Gabriela Diaz-Porto , Ismael Gutierrez \* and Armando Torres-Grandisson**

Department of Mathematics, Universidad del Norte, Km 5 via a Puerto Colombia, Barranquilla 081007, Colombia **\*** Correspondence: isgutier@uninorte.edu.co

**Abstract:** In this paper, we introduce *t*-graphs defined on finitely generated groups. We study some general aspects of the *t*-graphs on two-generator groups, emphasizing establishing necessary conditions for their connectedness. In particular, we investigate properties of *t*-graphs defined on finite dihedral groups.

**Keywords:** finitely generated groups; finite groups; *t*-graph; subgraph; connected components; chromatic number

**MSC:** 20F05; 20E65; 05C12; 05C15
