Remarks on Wiener Index of Bipolar Fuzzy Incidence Graphs

Fuzzy data plays an important role in daily life, and fuzzy structured data is usually represented by fuzzy graphs, where the graph structure is used to describe the associated structure of the fuzzy data. Based on the definition of Wiener index on bipolar fuzzy incidence graphs, this article continues to study the characteristics of this distance based topological index. The lower and upper bounds for positive and negative Wiener index of fuzzy bipolar incidence graph are determined respectively, and the relationship of Wiener index between original graph and its subgraph is discussed. The Wiener absolute index on bipolar fuzzy incidence graph is introduced accordingly, and several conclusions are determined in terms of geodesics distance analysis. Furthermore, we demonstrate the equality of Wiener index and Wiener absolute index for two isomorphic bipolar fuzzy incidence graphs.

Automated summary

This article investigates the Wiener index on bipolar fuzzy incidence graphs, determining the lower and upper bounds for positive and negative Wiener index, and discussing the relationship between the original graph and its subgraph. The Wiener absolute index is introduced, and conclusions are drawn in terms of geodesic distance analysis. Additionally, the equality of Wiener index and Wiener absolute index for two isomorphic bipolar fuzzy incidence graphs is demonstrated.