On integer sequences associated with the cyclic and complete graphs

Paul Barry

On integer sequences associated with the cyclic and complete graphs

Paul Barry

School of Science and Computing

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

We study integer sequences associated with the cyclic graph C_r and the complete graph K_r. 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.

Original language	English
Article number	07.4.8
Journal	Journal of Integer Sequences
Volume	10
Issue number	4
Publication status	Published - 04 May 2007

Keywords

Circulant matrices
Cyclic graphs
Discrete Fourier transform
Integer sequences
Jacobsthal numbers
Pascal's triangle

Cite this

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title = "On integer sequences associated with the cyclic and complete graphs",

abstract = "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.",

keywords = "Circulant matrices, Cyclic graphs, Discrete Fourier transform, Integer sequences, Jacobsthal numbers, Pascal's triangle",

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year = "2007",

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AB - 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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KW - Cyclic graphs

KW - Discrete Fourier transform

KW - Integer sequences

KW - Jacobsthal numbers

KW - Pascal's triangle

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SN - 1530-7638

IS - 4

M1 - 07.4.8

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On integer sequences associated with the cyclic and complete graphs

Abstract

Keywords

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