{"id":41236,"date":"2025-08-10T19:25:36","date_gmt":"2025-08-10T19:25:36","guid":{"rendered":"https:\/\/uomosul.edu.iq\/en\/computerscience\/?p=41236"},"modified":"2025-08-10T19:25:49","modified_gmt":"2025-08-10T19:25:49","slug":"1-247","status":"publish","type":"post","link":"https:\/\/uomosul.edu.iq\/en\/computerscience\/2025\/08\/10\/1-247\/","title":{"rendered":"master’s thesis by Student \u00a0Abbas Hassan Mstou"},"content":{"rendered":"

Discussion of a master’s thesis in the College of Computer Science and Mathematics – Department of Mathematics Sciences entitled:<\/p>\n

” <\/strong>N- idempotent divisors graph of commutative rings<\/strong>“<\/strong><\/p>\n

\u00a0<\/strong>\u00a0<\/strong>It was discussed in the discussion room at the Faculty of Computer Science and Mathematics at the University of Mosul on Sunday , 10 -8-2025.<\/p>\n

master’s thesis by Student \u00a0Abbas Hassan Mstou<\/strong><\/p>\n

under<\/strong> the supervision of<\/strong> Prof. Dr.<\/strong> Hussam Qasim Mohammed<\/strong> . <\/strong><\/p>\n

Let R be a commutative ring with identity 1\u22600. The idempotent divisor graph of R is the (simple) graph \u03a0( R) with two vertices a and b, then a is adjacent with b if and only if ab=e.<\/p>\n

We introduce in the work and study the n – idempotent divisors graph in the ring R when it is\u00a0 (simple) graph \u03a0_n (R) with the vertices R_n^*={a^n:a\u2208R} and two different elements a and b adjacent if ab=e, where e^2=e\u22601. For each \u03a0_n ( R ) induced sub-graph of \u03a0( R )=\u03a0_n ( R ). In this study we prove \u03a0_n (R) is connected and diam(\u03a0_n (R))\u22643, where R is reduced ring and we give a sufficient condition to \u03a0_n (R)=\u03a0_m (R) where n\u2260m, and we study 2-idempotent divisors graph when R direct product to any two local rings and used this result to find Hosoya polynomial and Wiener index.<\/p>\n

 <\/p>\n

The scientific committee included the following members:<\/strong><\/p>\n