Neutrosophic Quadratic Residues and Non-Residues

Abstract

In this paper, we present the Neutrosophic quadratic residues and nonresidues with their basic interpretation as graphs in an algebraic manner and analog to the algebraic graphs. We establish the Neutrosophic, number-theoretic, and graph-theoretic properties of the set of Neutrosophic quadratic residues and nonresidues, many of which mirror those of the classical quadratic residues and nonresidues of modulo an odd prime. These properties, especially the algebraic ones, are connected to algebraic graphs, and thus we conclude the paper by studying the structural properties of Neutrosophic quadratic residue and quadratic nonresidue graphs.

Keywords

• quadratic residues
• quadratic nonresidues
• neutrosophic quadratic residues
• neutrosophic quadratic nonresidues
• neutrosophic quadratic nonresidue graph