journal-of-discrete-mathematical-sciences-and-cryptography Journal of Discrete Mathematical Sciences and Cryptography 2169-0065 0972-0529 Taru Publications 10.47974/JDMSC-2375 Generalization geodetic number idealization ring Al-Labadi Manal Department of Mathematics, Faculty of Arts and Sciences, University of Petra, Amman, Jordan Almuhur Eman Department of Mathematics, Faculty of Arts and Sciences, Applied Science Private University, Amman, Jordan Khalil Shuker Department of Mathematics, College of Science, University of Basrah, Basrah, Iraq Almwail Huda Department of Mathematics, Faculty of Education for Women, University of Kufa, Kufa, Iraq 29 5 1957 1963 22 05 2026

This paper introduces m-geodetic graphs as a new concept and gives complete characterizations of perfectly m-geodetic zero-divisor graphs. Additionally, it provides necessary and sufficient conditions in various cases. Results of this kind are important in deepening our understanding of the structural properties of any given zero divisor graph associated with an idealization ring numbers in these structures. 

 Commutative ring Idealization rings Zero-divisor graph Domination number Geodetic number access open retracted no