IJPAM: Volume 113, No. 3 (2017)

Title

QUADRATIC RESIDUES GRAPHS

Authors

M. Rezaei$^1$, S.U. Rehman$^2$, Z.U. Khan$^2$, A.Q. Baig$^2$, M.R. Farahani$^3$
$^1$Department of Mathematics
Buein Zahra Technical University
Buein Zahra, Qazvin, IRAN
$^2$Department of Mathematics
COMSATS Institute of Information Technology
Attock, PAKISTAN
$^3$Department of Applied Mathematics
Iran University of Science and Technology
IRAN

Abstract

We introduce and study the graphs whose vertex set is reduced residue system $mod~n$ such that two distinct vertices $a$ and $b$ are adjacent provided that $a^2 \equiv b^2~(mod~n)$.

History

Received: December 10, 2016
Revised: January 17, 2017
Published: March 28, 2017

AMS Classification, Key Words

AMS Subject Classification: 13A15, 13F05.
Key Words and Phrases: Quadratic residues, complete graphs, union of graph.

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Bibliography

1
Kenneth H. Rosen, Elementry Number Theory and its Application, Addison-Wesley Publishing company (1984).

2
Hardy, G. H.; Wright, E. M., An Introduction to the Theory of Numbers (fifth ed.), Oxford: Oxford University Press (1980)

3
Ireland, Kenneth; Rosen, Michael, A Classical Introduction to Modern Number Theory (second ed.), New York: Springer (1990)

4
Lemmermeyer, Franz, Reciprocity Laws: from Euler to Eisenstein, Berlin: Springer (2000)

How to Cite?

DOI: 10.12732/ijpam.v113i3.8 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 113
Issue: 3
Pages: 465 - 470


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