Summary: Minimum Number of Distinct Eigenvalues of Cycles
In this document we prove that for any even cycle Cn, q(Cn) is equal to the diameter, i.e. n/2 and for
any odd cycle Cn, q(Cn) is equal to the diameter plus one, i.e. n/2 + 1.
Assume, first, that n 4 is even and consider the sequence of n×n matrices {I = B(0)
, B(1)
, B(2)
, . . .},
in which, for any k 1, we define
B
(k)
i,j =



B
(k-1)
i,j-1 + B
(k-1)
i,j+1 : 1 < j < n
B

Source: Argerami, Martin - Department of Mathematics and Statistics, University of Regina

Collections: Mathematics