Connectivity of Fibonacci cubes, Lucas cubes and generalized cubes
Copyright policy )Connectivity of Fibonacci cubes, Lucas cubes and generalized cubes
Graph Theory If f is a binary word and d a positive integer, then the generalized Fibonacci cube Qd(f) is the graph obtained from the d-cube Qd by removing all the vertices that contain f as a factor, while the generalized Lucas cube Qd(lucas(f)) is the graph obtained from Qd by removing all the vertices that have a circulation containing f as a factor. The Fibonacci cube Γd and the Lucas cube Λd are the graphs Qd(11) and Qd(lucas(11)), respectively. It is proved that the connectivity and the edge-connectivity of Γd as well as of Λd are equal to ⌊ d+2 / 3⌋. Connected generalized Lucas cubes are characterized and generalized Fibonacci cubes are proved to be 2-connected. It is asked whether the connectivity equals minimum degree also for all generalized Fibonacci/Lucas cubes. It was checked by computer that the answer is positive for all f and all d≤9.
- University of Ljubljana Slovenia
- University of Maribor Slovenia
- Faculty of Mathematics and Physics, University of Ljubljana Slovenia
- Incheon National University Korea (Republic of)
- University of Ljubljana, Faculty of Mathematics and Physics Slovenia
Fibonacci cube, Lucasova kocka, [info.info-dm] computer science [cs]/discrete mathematics [cs.dm], Fibonaccijeva kocka, [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], lucas cube, QA1-939, kombinatorika besed, combinatorics on words, [INFO.INFO-HC]Computer Science [cs]/Human-Computer Interaction [cs.HC], Lucas cube, info:eu-repo/classification/udc/519.17:004, generalized Fibonacci cube, povezanost, generalized lucas cube, [info.info-hc] computer science [cs]/human-computer interaction [cs.hc], fibonacci cube, posplošena Lucasova kocka, [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], generalized Lucas cube, connectivity, generalized fibonacci cube, [INFO.INFO-HC] Computer Science [cs]/Human-Computer Interaction [cs.HC], Mathematics, posplošena Fibonaccijeva kocka
Fibonacci cube, Lucasova kocka, [info.info-dm] computer science [cs]/discrete mathematics [cs.dm], Fibonaccijeva kocka, [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], lucas cube, QA1-939, kombinatorika besed, combinatorics on words, [INFO.INFO-HC]Computer Science [cs]/Human-Computer Interaction [cs.HC], Lucas cube, info:eu-repo/classification/udc/519.17:004, generalized Fibonacci cube, povezanost, generalized lucas cube, [info.info-hc] computer science [cs]/human-computer interaction [cs.hc], fibonacci cube, posplošena Lucasova kocka, [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], generalized Lucas cube, connectivity, generalized fibonacci cube, [INFO.INFO-HC] Computer Science [cs]/Human-Computer Interaction [cs.HC], Mathematics, posplošena Fibonaccijeva kocka
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