Generalized Pell graphs

In this paper, generalized Pell graphs Pi(n,k), k >= 2, are introduced. The special case of k = 2 are the Pell graphs Pi(n) defined earlier by Munarini. Several metric, enumerative, and structural properties of these graphs are established. The generating function of the number of edges of Pi(n,k) and the generating function of its cube polynomial are determined. The center of Pi(n,k) is explicitly described; if k is even, then it induces the Fibonacci cube Gamma(n). It is also shown that Pi(n,k) is a median graph, and that Pi(n,k) embeds into a Fibonacci cube.