2019/11/12 by Rachid Marsli, Marsli, Rachid, Frank J. Hall +1
Computer Science · Mathematics · #15A18 #15B51 #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1911.06139
openalex publication_date 2019/11/12 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
The main result is Corollary 2.9 which provides upper bounds on, and even\nbetter, approximates the largest non-trivial eigenvalue in absolute value of\nreal constant row-sum matrices by the use of vector norm based ergodicity\ncoefficients Tp. If the constant row-sum matrix is nonsingular, then it is also\nshown how its smallest non-trivial eigenvalue in absolute value can be bounded\nby using Tp. In the last section, these two results are applied to bound the\nspectral radius of the Laplacian matrix as well as the algebraic connectivity\nof its associated graph. Many other results are obtained. In particular,\nTheorem 2.15 is a convergence theorem for Tp and Theorem 4.7 compares some\nergodicity coefficients to each other.\n