On palindromes with three or four letters associated to the Markoff spectrum

Let N(2) and N(5) be the sets of integer solutions of 2x2+y12+y22=4xy1y2 and 5x2+y12+y22=5xy1y2, respectively. The elements of these sets give sequences in the non-discrete part of the Markoff spectrum consisting of the normalized values of arithmetic minima of indefinite quadratic forms. Each of these sets can be represented by a bipartite graph. Using this we can construct quadratic forms giving the values of the sequences. We show that, for a quadratic form f which gives a value of the Markoff spectrum corresponding to an integer solution x of N(2) and N(5), the roots of f(ξ,1)=0 have a periodic continued fraction expansion and the period is a palindrome with fixed prefix and suffix on {1,2,3} and {1,2,3,4}, respectively.