تقرير
On Hermitian Adjacency Matrices for Mixed Graphs
| العنوان: | On Hermitian Adjacency Matrices for Mixed Graphs |
|---|---|
| المؤلفون: | She, Tao, Wang, Chunxiang |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, 05C50, 15A18 |
| الوصف: | We study the spectra of mixed graphs about its Hermitian adjacency matrix of the second kind (i.e. N-matrix) introduced by Mohar [1]. We extend some results and define one new Hermitian adjacency matrix, and the entry corresponding to an arc from $u$ to $v$ is equal to the $k$-th( or the third) root of unity, i.e. ${\omega} = cos(2{\pi}/k) + \textbf{i} \ sin(2{\pi}/k), k {\geq} 3$; the entry corresponding to an undirected edge is equal to 1, and 0 otherwise. In this paper, we characterize the cospectrality conditions for a mixed graph and its underlying graph. In section 4, we determine a sharp upper bound on the spectral radius of mixed graphs, and provide the corresponding extremal graphs. Comment: 14 pages, 5 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2205.15584 |
| رقم الأكسشن: | edsarx.2205.15584 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |