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Applicable Analysis and Discrete Mathematics 2012 Volume 6, Issue 1, Pages: 82-94
https://doi.org/10.2298/AADM120108002I
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Generalized Lucas cubes

Ilić Aleksandar (Faculty of Sciences and Mathematics, Niš) Klavžar Sandi (Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia + Faculty of Natural Sciences and Mathematics, University of Maribor, Maribor, Slovenia) Rho Yoomi (Department of Mathematics University of Incheon, Korea)

Let f be is a binary string and d≥1. Then the generalized Lucas cube Qd(f¯)is introduced as the graph obtained from the 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(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.

Keywords: hypercube, Lucas cube, generalized Lucas cube, isometric embedding

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