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Extended Idempotent Divisor Graph of Zn | ||
| AL-Rafidain Journal of Computer Sciences and Mathematics | ||
| Article 21, Volume 18, Issue 2, December 2024, Pages 161-167 PDF (643.67 K) | ||
| Document Type: Research Paper | ||
| DOI: 10.33899/csmj.2024.153694.1146 | ||
| Authors | ||
| Husam Qasem mohammad* 1; Sumaya Mohammed2 | ||
| 1جامعة الموصل | ||
| 2university of Mosul | ||
| Abstract | ||
| Associate graph Л(R) is said to be idempotent divisor graph with vertices set in R*=R-{0} and two non- zero distinct vertices a and b are adjacent if and only if a.b=e, where e an idempotent element non equal 1. In this work we study the extended idempotent divisor graph of Zn is denoted by (Л(R)) ̅, with vertices set in R* that is for any two distinct vertices a and b are adjacent if there are positive integers t_1,t_2 such that a^(t_1 ). b^(t_2 )=e, where a^(t_1 ), b^(t_2 )≠ 0 and an idempotent element e not equal 1, and we found the order and the size for some kinds of the idempotent divisor graph of the rings Zn. Also, we found the Hosoya polynomial and the Wiener index for these graphs. | ||
| Keywords | ||
| extended idempotent divisor; zero divisor graph; idempotent divisor graph; Zn; Hosoya polynomial and the Wiener index | ||
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