Discussion of a master's thesis in the College of Computer Science and Mathematics - Department of Mathematics Sciences entitled:

"Extended Idempotent Divisor Graphs of A Commutative Rings"

It was discussed in the discussion room at the Faculty of Computer Science and Mathematics at the University of Mosul on Wednesday 17-11-2022

Master's thesis by student Sumaya  Mohammed Abd-almohy

, under the supervisor of Assistant Professor Dr. Husam Qasem Mohammad

.

   In this work we introduced an extended idempotent divisor graph as a simple graph  of a finite commutative ring  with vertices set in  and two distinct elements  V( ) adjacent if and only if there exists two positive integers  and  such that.  ,where  is an idempotent element not equal  and .

The aim of this work its to give some basic properties of an extended idempotent divisor  graph specially when  reduced ring, also we classify its graphs by using diameter as well as we find order, size and center. Finally we applied this concepts in a ring module n and we give a Hosoya polynomial and Wiener index of this graphs.

 

The scientific committee included the following members:

 

1- Prof. Dr. Nazar  Hamdoon  Shuker -Chairman

2- Asst. Prof. Zubaida  Mohammed  Ibraheem- Member

3- Asst. Prof. Dr. Payman  Abas  Rashed - Member

4- Professor Dr. Husam Qasem Mohammad - Advisor and Member

 

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