The Relation Between some Polynomials and the Wiener Index of Fuzzy Graphs

In this paper, the distance between two vertices in a fuzzy graph is defined in a new way. In addition, some new degree-based fuzzy graph polynomials are introduced. By using this definition, fuzzy graph polynomials, and a special lower triangular matrix, the Wiener index and the generalized Wiener index of a fuzzy graph are computed, which coincide with the Wiener index and the generalized Wiener index in the crisp graph. The result is used to compute the Wiener index of the sum, products, and composition of two fuzzy graphs.

کلیدواژه ها:

Fuzzy graph ، Fuzzy Wiener index ، Fuzzy graph degree-based polynomial