On Graph Primal Topological Spaces

In this paper, we introduce the concept of the “graph primal,” which serves as the dual structure to the “graph grill”. We present several results associated with graph primal operations. Moreover, we introduce two new graph-local functions on graph adjacency topological spaces (graph ATSs). We then explore the basic properties of the proposed graph-local functions and describe a method for generating two new graph ATSs from existing ones via graph primals. In addition, we examine several fundamental properties and connections of the resulting topologies, supported by some counterexamples. Furthermore, we characterize the nature of the open sets of these new topologies in terms of closure operators. Finally, we assess the compatibility of graph ATSs with the graph primal concept.