A note on the integer eigenvalues of the Laplacian matrix of a balanced binary tree Original Research Article

Let image be the Laplacian matrix of an unweighted balanced binary tree image of k levels. In this note, we show that 1. [(a)] λ=1 is an eigenvalue of image with multiplicityimagewhereimage is the greatest integer not exceeding (k−2)/4. 1. [(b)] λ=3 is an eigenvalue of image if and only if k is even. 2. [(c)] λ=5 is an eigenvalue of image if and only if k is a multiple of 4.