Constructing New Topological Graph with Several Properties

Abstract

In this paper, a new idea to configure a special graph from the discrete topological space is given. Several properties and bounds of this topological graph are introduced. Such that if the order of the non-empty set equals two, then the topological graph is isomorphic to the complete graph. If the order equals three, then the topological graph is isomorphic to the complement of the cycle graph. Our topological graph has n − 1 complete induced subgraphs with order n or more. It also has a cycle subgraph. In addition, the clique number is obtained. The topological graph is proved simple, undirected, connected graph. It has no pendant vertex, no isolated vertex and no cut vertex. The minimum and maximum degrees are evaluated. So, the radius and diameter are studied here.