Turkish Journal of Mathematics, cilt.47, sa.7, ss.1955-1973, 2023 (SCI-Expanded)
In this paper, generalized Pell graphs Πn,k, k ≥ 2, are introduced. The special case of k = 2 are the Pell graphs Πn defined earlier by Munarini. Several metric, enumerative, and structural properties of these graphs are established. The generating function of the number of edges of Πn,k and the generating function of its cube polynomial are determined. The center of Πn,k is explicitly described; if k is even, then it induces the Fibonacci cube Γn. It is also shown that Πn,k is a median graph, and that Πn,k embeds into a Fibonacci cube.