10 August، 2025
master’s thesis by Student Abbas Hassan Mstou
Discussion of a master’s thesis in the College of Computer Science and Mathematics – Department of Mathematics Sciences entitled:
” N- idempotent divisors graph of commutative rings“
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.
master’s thesis by Student Abbas Hassan Mstou
under the supervision of Prof. Dr. Hussam Qasim Mohammed .
Let R be a commutative ring with identity 1≠0. The idempotent divisor graph of R is the (simple) graph Π( R) with two vertices a and b, then a is adjacent with b if and only if ab=e.
We introduce in the work and study the n – idempotent divisors graph in the ring R when it is (simple) graph Π_n (R) with the vertices R_n^*={a^n:a∈R} and two different elements a and b adjacent if ab=e, where e^2=e≠1. For each Π_n ( R ) induced sub-graph of Π( R )=Π_n ( R ). In this study we prove Π_n (R) is connected and diam(Π_n (R))≤3, where R is reduced ring and we give a sufficient condition to Π_n (R)=Π_m (R) where n≠m, 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.
The scientific committee included the following members:
- Dr. Nazar Hamdoon Shuker – Chairman
- Dr. Ahmed Mohammed Ali – Member.
- Prof Dr. Barah Mahmood Sulaiman – Member.
- Dr. Hussam Qasim Mohammed – Member and supervisor.
