Graph Ideal Proximity Spaces

This paper focuses on extending the concept of "proximity" between sets to graphs. We define graph proximity, graph ideal-proximity spaces. Using the proposed graph ideal proximity spaces, we suggest a new operator over the vertices of a given graph and examine some of their essential aspects. As a result, we obtain a new topological spaces via this new operator over the vertices of a given graph. Comparisons between the obtained topology and old ones are presented. Further, we not only study some of its properties but also provide some examples. The properties and the implications of related definitions are proposed with examples. Near set theory supplies a major for the classification of members of a set in classes depending on there closeness. We follow the same idea in the graph theory. So, our definitions of graph proximities depend on the nearness of vertices of these graphs. that is we say that to graphs are near if there vertices are near. Based on the idea of nearness between vertices, a real-life application suggested from an information system is provided to demonstrate the significance of this research.