Hypercubes and Fibonacci cubes are classical models for interconnection networks with interesting graph theoretic properties. We consider [Formula: see text]-Fibonacci cubes, which we obtain as subgraphs of Fibonacci cubes by eliminating certain edges during the fundamental recursion phase of their construction. These graphs have the same number of vertices as Fibonacci cubes, but their edge sets are determined by a parameter [Formula: see text]. We obtain properties of [Formula: see text]-Fibonacci cubes including the number of edges, the average degree of a vertex, the degree sequence and the number of hypercubes they contain.

中文翻译：

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k-Fibonacci Cubes：Fibonacci Cubes 的子图族

超立方体和斐波那契立方体是具有有趣图论特性的互连网络的经典模型。我们考虑[公式：见正文]-斐波那契立方体，我们通过在其构造的基本递归阶段消除某些边缘来获得斐波那契立方体的子图。这些图具有与斐波那契立方体相同数量的顶点，但它们的边集由参数 [公式：参见文本] 确定。我们获得了[公式：见正文]-斐波那契立方体的属性，包括边数、顶点的平均度数、度数序列以及它们包含的超立方体的数量。