Journal of Integer Sequences, Vol. 15 (2012), Article 12.7.8

Fibonacci Numbers of Generalized Zykov Sums

César Bautista-Ramos and Carlos Guillén-Galván
Facultad de Ciencias de la Computación
Benemérita Universidad Autónoma de Puebla
14 Sur y Av. San Claudio, Edif. 104C, 303
Puebla, Pue. 72570


We show that counting independent sets in several families of graphs can be done within the framework of generalized Zykov sums by using the transfer matrix method. Then we calculate the generating function of the number of independent sets for families of generalized Zykov sums. We include many interesting particular cases (Petersen graphs, generalized Móbius ladders, carbon nanotube graphs, among others).

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(Concerned with sequences A003688 A007070 A007483 A026150 A028859 A050402 A051926 A051928 A078057 A161941 A181961 A181989 A182014 A182019 A182041 A182052 A182054 A182077 A182130 A182141 A182143 A188707.)

Received May 4 2012; revised versions received August 22 2012; September 13 2012. Published in Journal of Integer Sequences, September 23 2012.

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