Graphs as Topological spaces: A Study of Block Topology and its Basic Properties

Abstract

The interaction between graph theory and topology has yielded rich results for understanding many structural interpretations of discrete objects. This paper examines block spaces on undirected graphs. Fundamental concepts such as closure, density, and continuity were studied, and the conditions for connectedness were discussed, furthermore, the contractibility of block spaces and the fixed-point theory of continuous block-preserving functions were verified. Finally, the complete equivalence between topological homeomorphism and block-cut tee isomorphism were established.