Abstract Let f be a binary word and n ≥ 1 . Then the generalized Lucas cube Q n ( f ↽ ) is the graph obtained from the n -cube Q n by removing all vertices that have a circulation containing f as a factor. Ilic, Klavžar and Rho solved the question for which f and n , Q n ( f ↽ ) is an isometric subgraph of Q n 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 Q n ( f ↽ ) being an isometric subgraph of Q n are found, and two problems on generalized Lucas cubes are also listed.

中文翻译：

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等距词的圆形可嵌入性

摘要 令 f 是一个二进制字且 n ≥ 1 。然后广义卢卡斯立方体 Q n ( f ↽ ) 是从 n -立方体 Q n 通过删除所有具有包含 f 作为因子的循环的顶点获得的图。Ilic、Klavžar 和 Rho 解决了 f 和 n 的问题，Q n ( f ↽ ) 是 Q n 的等距子图，适用于所有长度最多为 5 的二进制字。本文进一步研究了这个问题。对于等距词 f ，找到了 Q n ( f ↽ ) 是 Q n 的等距子图的充要条件，并列出了广义 Lucas 立方体的两个问题。