On cycles in the sequence of unitary Cayley graphs
type: Item
instance of: scholarly article
title: On cycles in the sequence of unitary Cayley graphs
zbMATH Open document ID: 1055.05087
author: Pedro Berrizbeitia
author: Reinaldo E. Giudici
published in: Discrete Mathematics
publication date: 2004-08-06T00:00:00Z
review text: The authors prove the following results. (1) Given \(r\in N\), there is \(N(r)\in N\), depending only on \(r\), such that \(p_k(n)=0\) for all \(k\geq N(r)\) and for all \(n\) with at most \(r\) different prime divisors. (2) For every \(r\) there are non-trivial arithmetic functions \(f\) satisfying the following two properties: (i) \(f\) is a \(Z\)-linear combination of multiplicative arithmetic functions, and (ii) \(f(n)=0\) for every \(n\) with at most \(r\) different prime divisors.
Mathematics Subject Classification ID: 05C38
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 2083700
zbMATH Keywords: Cayley graphs
zbMATH Keywords: Induced \(k\)-cycles of a graph
zbMATH Keywords: Group of units
zbMATH Keywords: Arithmetic functions
zbMATH Keywords: Chromatic polynomial uniqueness
reviewed by: Chunhui Lai
MaRDI profile type: Publication
full work available at URL: j.disc.2003.11.013
OpenAlex ID: W2015378916
cites work: Chromatic polynomials and whitney's broken circuits
cites work: Counting pure \(k\)-cycles in sequences of Cayley graphs
cites work: Chromatic Polynomials
cites work: On chromatic coefficients
cites work: The chromatic uniqueness of certain broken wheels
cites work: Coefficients of chromatic polynomials
cites work: On the chromatic uniqueness of certain bipartite graphs
cites work: Approximate formulas for some functions of prime numbers
DOI: 10.1016/J.DISC.2003.11.013
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description: scientific article; zbMATH DE number 2083700