Nano topology induced by graphs

Abstract

The aim of this paper is to introduce new subgraph types related to given subgraphs of a graph G. Specifically, these are termed c-subgraph, i-subgraph, and bsubgraph of a subgraph H from G, denoted as cH, iH, and bH, respectively. The paper explores various properties and results concerning these new subgraph types and their complements under certain binary operations. Additionally, it introduces a new type of nano topological space known as a nano graph topological space, defined in terms of these new subgraph types. The study also investigates properties of nano closure and nano interior subgraphs.