Application of Second Zagreb Index on Bipolar Fuzzy Graphs

ZainAlabdeen .M Lafta; Ali Asghar Talebi

doi:10.65463/jprm.2026274.

Authors

ZainAlabdeen .M Lafta Department of Mathematics, University of Mazandaran, Babolsar, Iran.
Ali Asghar Talebi Department of Mathematics, University of Mazandaran, Babolsar, Iran.

DOI:

https://doi.org/10.65463/jprm.2026274.

Keywords:

Fuzzy Graph, Bipolar Fuzzy Graph, Second Zagreb Index, Topological Index.

Abstract

The Zagreb indices are important topological tools in mathematical chemistry and network analysis. This article presents a novel extension of the second Zagreb index to the domain of bipolar fuzzy graphs, a powerful structure for modeling systems with opposing or ambivalent interactions. We formally define the bipolar second Zagreb index and explore its theoretical foundations by calculating its values and bounds for standard bipolar fuzzy graphs like paths, cycles, and stars. We get the bounds for this index under complex graph operations-Cartesian product, composition, join, and union-which are essential for constructing sophisticated network models. This work not only enriches fuzzy graph theory but also provides a foundational tool for quantitatively analyzing bipolarity social. Finally, we present on Application of second Zagreb index to find the most suitable place to build a hospital.

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