On Vertex Eccentricity Labeled Energy of A Graph

  • Authors

    https://doi.org/10.14419/qtfv0860

    Received date: June 19, 2025

    Accepted date: August 7, 2025

    Published date: August 12, 2025

  • Eccentricity; Graph Energy; Vertex Eccentricity Labeled Energy

  • Abstract

    In this paper, we introduce a new spectral graph invariant called the Vertex Eccentricity Labeled Energy (VELE). VELE is derived from the ‎eigenvalues of the Vertex Eccentricity Labeled (VEL) matrix, whose off-diagonal entries for a connected graph G are defined as the sum of ‎eccentricities of vertex pairs, and zero otherwise. We explore fundamental algebraic and spectral properties of VELE, including its trace, ‎characteristic polynomial, and energy bounds. Closed-form formulas for VELE are provided for several classical graph families, such as ‎complete graphs, cycles, wheels, and stars. Additionally, the behavior of VELE is studied under common graph operations such as Cartesian product, splitting, and m-splitting, highlighting distinctive spectral patterns related to vertex eccentricity. These results expand the family ‎of spectral descriptors and offer new analytical tools in structural graph analysis‎.

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  • How to Cite

    Gusai, S., Kaneria, V., & Jadeja, M. (2025). On Vertex Eccentricity Labeled Energy of A Graph. International Journal of Basic and Applied Sciences, 14(4), 339-350. https://doi.org/10.14419/qtfv0860