On cyclic topological spaces of graphs

Abstract

This paper introduces the innovative concept of cyclic topological
spaces for simple graphs, leveraging cyclic subgraphs to define
$C$-vertices. We delve into several properties within these
topologies, providing a foundational study. A significant
contribution is the establishment of a rigorous framework proving
the correspondence between graph isomorphisms and homeomorphisms in
cyclic topological spaces. Furthermore, we explore the connectedness
of these spaces and its profound implications for graph theory,
enhancing our understanding of structural relationships in both
fields.