On the domination number and the 2-packing number of Fibonacci cubes and Lucas cubes

Authors:
Aline Castro;Sandi Klavar;Michel Mollard;Yoomi Rho
Affiliations:
Institut Fourier, UJF - CNRS, 100, rue des Maths, BP 74, 38402 St Martin d'Hères Cedex, France;Faculty of Mathematics and Physics, University of Ljubljana, Slovenia and Faculty of Natural Sciences and Mathematics, University of Maribor, Slovenia;Institut Fourier, UJF - CNRS, 100, rue des Maths, BP 74, 38402 St Martin d'Hères Cedex, France;Department of Mathematics, University of Incheon, Republic of Korea
Venue:
Computers & Mathematics with Applications
Year:
2011

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Abstract

Let @C"n and @L"n be the n-dimensional Fibonacci cube and Lucas cube, respectively. The domination number @c of Fibonacci cubes and Lucas cubes is studied. In particular it is proved that @c(@L"n) is bounded below by @?L"n-2nn-3@?, where L"n is the nth Lucas number. The 2-packing number @r of these cubes is also studied. It is proved that @r(@C"n) is bounded below by 2^2^^^@?^^^l^^^g^^^n^^^@?^^^2^^^-^^^1 and the exact values of @r(@C"n) and @r(@L"n) are obtained for n@?10. It is also shown that Aut(@C"n)~Z"2.