Abstract

Let f be a binary word and n≥1. Then the generalized Lucas cube Qn(f↽) is the graph obtained from the n-cube Qn by removing all vertices that have a circulation containing f as a factor. Ilić, Klavžar and Rho solved the question for which f and n, Qn(f↽) is an isometric subgraph of Qn for all binary words of length at most five. This question is further studied in this paper. For an isometric word f, sufficient and necessary conditions of Qn(f↽) being an isometric subgraph of Qn are found, and two problems on generalized Lucas cubes are also listed.

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