2023/02/27 by Mahdi Ebrahimi, Ebrahimi, Mahdi
Chemistry · Mathematics · #05C50 #05C76 #05E10 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Synthesis and Properties of Aromatic Compounds
paper · pdf · doi:10.48550/arxiv.2303.01304
openalex publication_date 2023/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We first describe a system of inequalities (Horn's inequalities) that characterize eigenvalues of sums of Hermitian matrices. When we apply this system for integral Hermitian matrices, one can directly test it by using Littlewood-Richardson coefficients. In this paper, we apply Horn's inequalities to analysis the eigenvalues of an integral line graph G of a connected bipartite graph. Then we show that the diameter of G is at most 2ω(G), where ω(G) is the clique number of G. Also using Horn's inequalities, we show that for every odd integer k≥ 19, a non-complete k-regular Ramanujan graph has an eigenvalue less than -2.