Eccentricity-Based Bounds for the Spectral Radius of Graph Matrices

Sunilgar Gusai

Abstract: This article presents a framework for bounding the spectral radius of classical graph matrices, specifically the adjacency and signless Laplacian matrices, using vertex eccentricity as a global structural parameter. By applying the Collatz-Wielandt characterization and Rayleigh quotient methods with the eccentricity vector as a test input, the study derives both upper and lower bounds that incorporate global distance distributions. The proposed bounds are shown to be sharp for regular and self-centered graph families and remain useful for irregular structures. Through these results, eccentricity emerges as a complementary control parameter to degree-based approaches, providing enhanced insight into how both local and global structures shape spectral behaviour.

Keywords: Spectral radius, vertex eccentricity, adjacency matrix, signless Laplacian matrix, Collatz?Wielandt inequality

How to Cite?: Sunilgar Gusai, "Eccentricity-Based Bounds for the Spectral Radius of Graph Matrices", Volume 15 Issue 1, January 2026, International Journal of Science and Research (IJSR), Pages: 681-686, https://www.ijsr.net/getabstract.php?paperid=SR26109233300, DOI: https://dx.doi.org/10.21275/SR26109233300