Arya Bhatta Journal of Mathematics and Informatics
  • Year: 2017
  • Volume: 9
  • Issue: 2

Perron number of a cyclotomic graph

  • Author:
  • A. Ramesh Kumar1,, D. Nagarajan2,
  • Total Page Count: 6
  • Page Number: 343 to 348

1Head, Department of Mathematics, Srimad Andavan Arts & Science College (Autonomous), Trichy

2Asst. Professor, Department of Mathematics, Srimad Andavan Arts & Science College (Autonomous), Trichy

*E-mail: andavanmathsramesh@gmail.com

**nagarajanmathematics@gmail.com

Online published on 18 October, 2017.

Abstract

We define Cyclotomic matrix and Cyclotomic graph. For A an integer symmetric matrix, all roots of A(x) are real algebraic integers and RA(z) is cyclotomic if A has spectral radius at most 2. If the Mahler measure of A is 1, then A is a cyclotomic matrix. We find the Perron number of the graphs whose adjacency matrices are the symmetric matrices having all its entries from the set {0, 1} and only zeros on the diagonal.

Keywords

Perron Number, Mahler Measure, Cyclotomic graph