Remarks on bipolar cubic fuzzy graphs and its chemical applications

Abstract

In theoretical chemistry, fuzzy molecular graphs can be used to model chemical molecular structures with uncertainty information, where the vertex membership function and edge membership function describe the uncertainty of atoms and chemical bonds respectively. This paper studies chemical topological index of bipolar cubic fuzzy graphs. The new concepts and theorems are given in terms of graph theory and fuzzy set theory approaches and several theoretical conclusions on bipolar Wiener index of bipolar cubic fuzzy graphs are determined. Furthermore, we apply it in chemical science and calculate the bipolar Wiener index of dimethyltryptamine and hallucinogen which are modelled by bipolar cubic fuzzy graphs.

Embedding Spanning Disjoint Cycles in Hypercube Networks with Prescribed Edges in Each Cycle

“…Graph theory is also applied to the many field such as chemistry, electrical, neural network and so on. Lu et al used fuzzy molecular graphs to model chemical molecular structures with uncertainty information, where the vertex membership function and edge membership function describe the uncertainty of atoms and chemical bonds respectively [1]. In [2], Wang et al used the relevant theories of graph theory to construct the electrical equipment control relations matrix of process enterprises based on analyzing the characteristics of electrical equipment faults and control relations.…”

The Modulation Instability Analysis and Analytical Solutions of the Nonlinear Gross−Pitaevskii Model with Conformable Operator and Riemann Wave Equations via Recently Developed Scheme

“…Some control problems and optimization application have been presented [39][40][41][42][43][44][45]. In [46], bipolar cubic fuzzy graphs have been studied. The shallow ocean-waves and rogue waves with translational coordination have been observed in [47,48].…”

On interval-valued vector variational-like inequalities and vector optimization problems with generalized approximate invexity via convexificators

“…While talking about the practical application it is not easy to find the membership function related to the fuzzy set, but it is easy to find the membership degree of the interval value. Thus, this gives us a new technique for sequencing of fuzzy numbers of interval value, which gets the common model of interval valued fuzzy linear programming problem, and then solves corresponding problems, see for examples [16,31]. However, In the method of optimization known as the interval-valued optimization problem, the coefficients of both the objective and constraint functions are represented by closed intervals.…”