On the Forgotten Index and Jacobson Graphs Associated with Integer Rings Modulo n - Jauhari, Mohammad Nafie; Jannah, Shahnaz Latifatul; Turmudi, Turmudi; Nisfulaila, Intan (Jurusan Matematika, Fakultas Sains dan Teknologi, UIN Sunan Gunung Djati Bandung, 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.