Journal of Integer Sequences, Vol. 10 (2007), Article 07.4.8

On Integer Sequences Associated With the Cyclic and Complete Graphs

Paul Barry
School of Science
Waterford Institute of Technology


We study integer sequences associated with the cyclic graph Cr and the complete graph Kr. Fourier techniques are used to characterize the sequences that count walks of length n on both these families of graphs. In the case of the cyclic graph, we show that these sequences are associated with an induced colouring of Pascal's triangle. This extends previous results concerning the Jacobsthal numbers.

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(Concerned with sequences A000302 A001045 A001145 A006516 A007582 A015518 A015521 A015531 A020522 A052964 A054878 A078008 A084179 A109499 A109500 and A112798 .)

Received September 19 2005; revised version received April 26 2007. Published in Journal of Integer Sequences, May 4 2007.

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