An alternative construction of the $G_2(2)$-graph

TL;DR

This paper presents a new way to construct the $G_2(2)$-graph using a $U_3(2)$-geometry, offering an alternative perspective on its structure.

Contribution

It introduces a novel construction method for the $G_2(2)$-graph based on $U_3(2)$-geometry, expanding understanding of its geometric origins.

Findings

Provides an explicit alternative construction of the $G_2(2)$-graph.

Connects the graph to $U_3(2)$-geometry.

Enhances geometric understanding of the $G_2(2)$-graph.

Abstract

In this note, we give an alternative construction of the $G_2(2)$-graph from a $U_3(2)$-geometry.