In this paper we create a new topological structure induced by connected simple undirected graphs called maximal block topological space and study some properties of this new type of topology. Also, define some concepts in maximal block topological space like (derived subgraph, closure subgraph and interior subgraph). Some results and properties of vertices and subgraphs in G due to maximal block topological space are proved and discussed. Moreover, showed that a maximal block topological space is T0-space and T1/2-space if and only if G is acyclic graph. Finally, irreducibility and topologically independent of maximal block topological space are introduced.
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