Some Properties of the Connectivity Index in Vague Graphs with Application

In this paper, we first introduce simple fuzzy graphs (VGs), vague graphs, and then focus on one of the important indices of vague fuzzy graphs, namely the connectivity index, which measures the degree of coordination among the vertices of a graph. We apply this index to study the degree of coordination among the campuses and higher education centers of Farhangian University in Mazandaran Province, which are considered as the nodes of a vague fuzzy graph. The main question is whether these campuses and centers operate as a coordinated network or not. The membership functions of the vertices (nodes) are determined on the basis of the data of the Evaluation and Supervision Office of Farhangian University in Mazandaran Province, obtained mainly from student questionnaires in different domains such as the president’s office, administration, finance, research, cultural affairs and student services. At the end of the paper we conclude that the campuses and centers of Farhangian University do not yet behave as a perfectly coordinated network; however, by implementing the changes and improvements suggested in this paper they can become fully coordinated. Likewise, some new indices such as Zagreb index, sombor index, wiener index, and average wiener index are introduced.

کلیدواژه ها:

Vague fuzzy graph ، Connectivity index ، Application