Graph of a Nearring with Respect to an Ideal

Abstract

We introduce a concept called the graph of a nearring N with respect to an ideal I of N denoted by G I (N). Then we define a new type of symmetry called ideal symmetry of G I (N). The ideal symmetry of G I (N) implies the symmetry determined by the automorphism group of G I (N). We prove that if I is a 3-prime ideal of a zero-symmetric nearring N then G I (N) is ideal symmetric. Under certain conditions, we find that if G I (N) is ideal symmetric then I is 3-prime. Finally, we deduce that if N is an equiprime nearring then the prime graph of N is ideal symmetric.