论文信息 - On median nature and enumerative properties of Fibonacci-like cubes

On median nature and enumerative properties of Fibonacci-like cubes

Fibonacci cubes, extended Fibonacci cubes, and Lucas cubes are induced subgraphs of hypercubes defined in terms of Fibonacci strings. It is shown that all these graphs aremedian. Several enumeration results on the number of their edges and squares are obtained. Some identities involving Fibonacci and Lucas numbers are also presented. © 2005 Elsevier B.V. All rights reserved.

Sandi Klavzar

[1] Norma Zagaglia Salvi,et al. Structural and enumerative properties of the Fibonacci cubes , 2002, Discret. Math..

[2] W.-J. Hsu,et al. FIBONACCI CUBES—A CLASS OF SELF-SIMILAR GRAPHS , 1993 .

[3] Norma Zagaglia Salvi,et al. Observability of the extended Fibonacci cubes , 2003, Discret. Math..

[4] Pavol Hell,et al. Absolute retracts in graphs , 1974 .

[5] Emanuele Munarini,et al. On the Lucas cubes , 2001 .

[6] Martyn Mulder,et al. The structure of median graphs , 1978, Discret. Math..

[7] Jie Wu. Extended Fibonacci Cubes , 1997, IEEE Trans. Parallel Distributed Syst..

[8] H. M. Mulder. The interval function of a graph , 1980 .

[9] Hans-Jürgen Bandelt,et al. Retracts of hypercubes , 1984, J. Graph Theory.

[10] Petra Zigert,et al. FIBONACCI CUBES ARE THE RESONANCE GRAPHS OF FIBONACCENES , 2003 .

[11] Michael E. Saks,et al. Dynamic Search in Graphs , 1987 .

[12] W. Imrich,et al. Product Graphs: Structure and Recognition , 2000 .

[13] Wen-Jing Hsu,et al. Generalized fibonacci cubes are mostly hamiltonian , 1994, J. Graph Theory.

[14] Ernesto Dedó,et al. The observability of the Fibonacci and the Lucas cubes , 2002, Discret. Math..

[15] Alexander Schrijver,et al. Median graphs and Helly hypergraphs , 1979, Discret. Math..