Discussiones Mathematicae Graph Theory 33(3) (2013)
531-557

doi: 10.7151/dmgt.1707

Reinhardt Euler
Université Européenne de Bretagne and Lab-STICC, CNRS, UMR 6285 | Paweł Oleksik
AGH University of Science and Technology |
Zdzisław Skupień
AGH Kraków |

**Keywords:** independent set, grid graph, Fibonacci, Padovan numbers, transfer matrix method

**2010 Mathematics Subject Classification:** 11B39, 11B83, 05A15, 05C69.

[1] | R. Euler, Fibonacci number of a grid graph and a new class of integer sequences,
J. Integer Seq. 8 (2005) Article 05.2.6. |

[2] | Z. Füredi, The number of maximal independent sets in connected graphs, J. Graph Theory 11 (1987) 463?470. |

[3] | Z. Skupień, Independence or domination. Positioning method in recursive counting on paths or cycles, a manuscript (2012). |

[4] | N.J.A. Sloane, The On-line Encyclopedia of Integer Sequences, (2007). www.research.att.com/˜njas/sequences/ |

[5] | R.P. Stanley, Enumerative Combinatorics (Cambridge Univ. Press, vol. 1, 1997), doi: 10.1017/CBO9780511805967 |

Received 31 January 2012

Revised 11 October 2012

Accepted 5 November 2012