JACOBSON GRAPH OVER RING ZN - Zulfikar Aditya Nurl, Mochammad
Let be given a Zn ring for unknown n. Jacobson Graph over ring Zn is a graph with the vertex set of all the elements in Zn except the Jacobson Radical with the connected rules : x and y are neighbours if and only if 1 ???? xy is not relative prime to n. The characteristic of the Jacobson graph over those rings will be studied as the foundation of other Jacobson graph over another ring which is the direct sum of a few modulo rings. The connectedness and the shape of the Jacobson graph will be determined by the prime factors of n. One of the methods to determine the shape of the Jacobson graph over Zn is to see another graph over some ring that is equivalent to quotient ring of Zn=J(Zn) and it can help to find the other characteristics. In this final project, will be studied what n can be given to have some of the graph characterization such as diameter, planarity, and Hamiltonian graph. And also, will determined how to count the number of neighbors in every point on the graph.