A Study of Definition, Motivation and Properties of Combinatorial Curvature | Original Article

ABSTRACT:

We embrace a novel topological approach for graphs, in which edges are demonstrated as points instead of circular segments. The model of classical topologized graphs makes an interpretation of graph isomorphism into topological homeomorphism, with the goal that every combinatorial idea are expressible in simply topological dialect. This enables us to extrapolate ideas from finite graphs to infinite graphs furnished with a perfect topology, which, dropping the classical necessity, require not be remarkable. We convey standard ideas from general topology to tons of a combinatorial motivation, in an infinite setting. We indicate how (perhaps finite) graph-theoretic paths are, with no specialized subterfuges, a subclass of a general classification of topological spaces, to be specific paths, that incorporates Hausdorff bends, the genuine line and all associated orderable spaces (of discretionary cardinality).