Properties of Connectivity in Vague Fuzzy Graphs With Application in Building University

Graphs are used to solve many problems in mathematics and computer sciences. Many structures can be displayed with the help of graphs. For example, a directed graph can be used to show how websites are related to cach other. Vague graph (VG) is one of the most important graphs in the fuzzy graph (FG)-theory, which can play a significant role in finding the most suitable places in construction and also finding the shortest path in computer networks. Connectivity indices are one of the most widely used topics in graph theory, which are used in other sciences, including computer science and chemistry. One of the most famous indices in the graph is the Wiener index, which belongs to the description of the molecular structure, which is used to design molecules with desirable properties. Therefore, in this paper, we introduce important topological indices such as Wiener index, Wiener absolute index, Randic index, Zegreb index, Harmonic index, and Average Wiener index on VGs and investigate their properties with several examples. Finally, an application of the Wiener index is given to find the most suitable place to build an university.