2018/06/18 by Monimala Nej, Nej, Monimala, A. Satyanarayana Reddy +1
Computer Science · Engineering · Mathematics · #05C38 #05C50 #15B99 #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics #Matrix Theory and Algorithms #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1806.06838
openalex publication_date 2018/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A \it symmetric companion matrix is a matrix of the form A +AT where A is a companion matrix all of whose entries are in \0,1\ and AT is the transpose of A. In this paper, we find the total number of primitive and the total number of imprimitive symmetric companion matrices. We establish formulas to compute the exponent of every primitive symmetric companion matrix. Hence the exponent set for the class of primitive symmetric companion matrices is completely characterized. We also obtain the number of primitive symmetric companion matrices with a given exponent for certain cases.