Appl. Anal. Discrete Math. 6 (2012), 82–94. doi:10.2298/AADM120108002I GENERALIZED LUCAS CUBES

f) is introduced as the graph obtained from the d-cube Qd by removing all vertices that have a circulation containing f as a substring. The question for which f and d, the generalized Lucas cube Qd( ↽Ð f) is an isometric subgraph of the d-cube Qd is solved for all binary strings of length at most five. Several isometrically embeddable and non-embeddable infinite series where f is of arbitrary length are given. Some structural properties of generalized Lucas cubes are also presented. 1