On Vertex Eccentricity Labeled Energy of A Graph
Year: 2025
Type: article
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.
DOI: 10.14419/qtfv0860
Institutions: Marwadi University, Saurashtra University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4413194231