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.
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.
Perron Number, Mahler Measure, Cyclotomic graph