Effects of Duplication Operations on Signless Laplacian Spectrum and Network Measures

Abstract

This article investigates the spectral properties of graphs under vertex and edge duplication,
analyzing how these operations affect the eigenvalues of Signless Laplacian operators. We derive the spectra
for graphs with duplicated vertices and edges, and evaluate key invariants such as Kirchhoff index, global
mean-first passage time, and spanning tree counts. Our results link structural graph transformations to their
spectral outcomes, offering insights for graph-based modeling in network science.