Continuity of Functions on Bare Representation of Graphs under Star Topology

Abstract

This paper introduces a novel topology, referred to as the star topology, on finite graphs. By treating vertices and edges as points in a unified space, we explore continuous maps between Bare representations of a graph and their properties. The key distinction lies in the fact that while every graph homomorphism induces a continuous map, the converse is not generally true due to potential loss of adjacency information.