On the Forgotten Index and Jacobson Graphs Associated with Integer Rings Modulo n - Jauhari, Mohammad Nafie; Jannah, Shahnaz Latifatul; Turmudi, Turmudi; Nisfulaila, Intan (KUBIK: Jurnal Publikasi Ilmiah Matematika, 2024)
This paper investigates the connections between the Jacobson graph and the algebraic properties of rings through the analysis of the Jacobson graph of the ring Z_3p, where p is a prime number greater than 3. The Jacobson graph of a commutative ring R is constructed by taking the elements of R, excluding its Jacobson Radical, as vertices, and connecting two distinct vertices if 1 minus their product is not a unit in R. The F-Index is utilized to capture and represent the structural properties of the ring through its associated graph. A detailed examination of the Jacobson Radical, maximal ideals, and vertex degrees in Z_3p leads to the calculation of the F-Index, providing insights into the graph’s connectivity and underlying algebraic structure. This study contributes to the intersection of algebra and graph theory, offering a foundation for further research into more complex algebraic structures.