This research uncovers graph properties, such as decomposition and Wiener index, in induced subgraphs of Fibonacci and Lucas cubes, indicating new avenues for exploration.
The Fibonacci cube [Formula: see text] can be obtained from the hypercube [Formula: see text] by removing all vertices that contain [Formula: see text] as a substring, and the Lucas cube [Formula: see text] can be obtained from [Formula: see text] by removing all the vertices that have a circulation containing [Formula: see text]. Let [Formula: see text] be an induced subgraph of [Formula: see text], then the cube-complement of [Formula: see text], denoted by [Formula: see text], is the graph induced by the vertices of [Formula: see text] which are not in [Formula: see text]. In this paper, we give a research on some aspects of [Formula: see text] and [Formula: see text], including the size, the decomposition, the degree sequence, the center and radius, the periphery and diameter, the medianicity, the (peripheral) Wiener index, and the cube polynomial. Several problems are also listed.
No takes yet. Share an insight, caveat, or question.
Wei et al. (2025) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: