The t-Graphs Over Finitely-Generated Groups and the Minkowski Metric

TL;DR

This paper introduces t-graphs on finitely-generated groups, explores their properties especially in 2-generator groups, and examines connectedness conditions with a focus on finite dihedral groups.

Contribution

It is the first to define and analyze t-graphs on finitely-generated groups, providing new insights into their structure and connectedness properties.

Findings

Necessary conditions for t-graph connectedness established

Properties of t-graphs on finite dihedral groups analyzed

Insights into the structure of t-graphs on 2-generator groups

Abstract

In this paper, we introduce the t-graphs defined on finitely-generate groups. We study some general aspects of the t-graphs on 2-generator groups, emphasising establishing necessary conditions for their connectedness. In particular, we investigate the properties of t-graphs defined on finite dihedral groups.