(untitled) (European Journal of Pure and Applied Mathematics, 2024)
Let G=(V(G),E(G)) be a simple undirected graph. A block of G is a maximal connected subgraph of G that contains no cut-vertices eric. The family of vertex sets of blocks of G generates a unique topology. In this paper, we formally define the topology generated by the family of blocks in a graph called the block topological space. Moreover, we characterize and describe some special attributes of the block topological space. Finally, we associate a corresponding graph from a given block topological space by defining the block topological graph.