Laplacian spectra and structural insights: applications in chemistry and network science - Raza, Ali; Mobeen Munir, Muhammad (Frontiers in Applied Mathematics and Statistics, 2025)
This paper presents the practical applications of Laplacian and signless Laplacian spectra across various fields including theoretical chemistry, computer science, electrical engineering, and complex network analysis. By focusing on the spectrum-based evaluation of generalized mesh network and ladder graphs, the research aims to uncover valuable relationships with the structural properties of real-world networks. The study not only explores the theoretical underpinnings but also applies these spectra to calculate essential network measures such as mean-first passage time, average path length, spanning trees, and spectral radius. These analyses offer a deeper understanding of how graph spectra influence network characteristics, enriching our ability to predict and analyze complex networks. This comprehensive approach enhances our knowledge across multiple scientific disciplines, facilitating more informed predictions about drugs infrastructure.