2023/05/04 by Gi‐Sang Cheon, Bumtle Kang, Cheon, Gi-Sang +5
Engineering · Mathematics · #05C20 #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2305.02690
openalex publication_date 2023/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In this paper, we study row graphs of Toeplitz matrices. The notion of row graphs was introduced by Greenberg et al. in 1984 and is closely related to the notion of competition graphs, which has been extensively studied since Cohen had introduced it in 1968. To understand the structure of the row graphs of Toeplitz matrices, which seem to be quite complicated, we have begun with Toeplitz matrices whose row graphs are triangle-free. We could show that if the row graph G of a Toeplitz matrix T is triangle-free, then T has the maximum row sum at most 2. Furthermore, it turns out that G is a disjoint union of paths and cycles whose lengths cannot vary that much in such a case. Then we study (0, 1)-Toeplitz matrices whose row graphs have only path components, only cycle components, and a cycle component of specific length, respectively. In particular, we completely characterize a (0, 1)-Toeplitz matrix whose row graph is a cycle.