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2020 Connectedness of digraphs from quadratic polynomials
Siji Chen, Sheng Chen
Involve 13(2): 357-360 (2020). DOI: 10.2140/involve.2020.13.357

Abstract

Suppose that f(x)=x(xk), where k is an odd positive integer. First, an infinite digraph Gk=(V,E) is defined, where the vertex set is V= and the edge set is E={(x,y)x,y,f(x)=f(2y)}. Then the following results are proved: if k=1, then the digraph Gk is weakly connected; if p is a safe prime, i.e., both p and q=(p1)2 are primes, then the number wp of weakly connected components of the digraph Gp is 2. Finally, a conjecture that there are infinitely many primes p such that wp=2 is presented.

Citation

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Siji Chen. Sheng Chen. "Connectedness of digraphs from quadratic polynomials." Involve 13 (2) 357 - 360, 2020. https://doi.org/10.2140/involve.2020.13.357

Information

Received: 2 February 2020; Revised: 10 March 2020; Accepted: 14 March 2020; Published: 2020
First available in Project Euclid: 25 June 2020

zbMATH: 07184489
MathSciNet: MR4080499
Digital Object Identifier: 10.2140/involve.2020.13.357

Subjects:
Primary: 05C25
Secondary: 05C20‎, 05C40

Rights: Copyright © 2020 Mathematical Sciences Publishers

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