Bipolar intuitionistic fuzzy graphs (BIFG) are an extension of fuzzy graphs that can effectively capture uncertain or imprecise information in various applications. In graph theory, the covering, matching, and domination problems are benchmark concepts applied to various domains. These concepts may not be defined precisely using a crisp graph when the vertices and edges are more uncertain. Therefore, this study defines the covering, matching and domination concepts in bipolar intuitionistic fuzzy graphs (BIFG) using effective edges with certain important results. To define these concepts when the effective edges are absent, some novel approaches are discussed. To illustrate the domination concepts, the applications in disaster management and location selection problems are discussed. Further, a BIFG-based decision-making model is designed to identify the flood-vulnerable zones in Chennai, where the city's most and least vulnerable zones are identified. From the proposed model, Kodambakkam ([Formula: see text]) is the most susceptible zone in Chennai. Finally, a comparative analysis is done with the existing techniques to show the efficiency of the model.
Keywords: Bipolar intuitionistic fuzzy graph; Covering; DEMATEL method; Effective edge; Graph domination; Matching.
© 2023. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.