Two Involution Clean Rings with Applications in Graph Theory

Ali Mohammed  Hassan; Raeda  Dawood; Mohammed Dhunoun  Al-Naama

doi:10.24996/ijs.2026.67.1.27

Authors

Ali Mohammed Hassan Department of Mathematics, College of Computer Science and Mathematics, University of Mosul, Mosul, Iraq
Raeda Dawood Department of Mathematics, College of Computer Science and Mathematics, University of Mosul, Mosul, Iraq https://orcid.org/0000-0002-4381-0869
Mohammed Dhunoun Al-Naama Department of Civil Engineering, College of Engineering University of Mosul, Mosul, Iraq https://orcid.org/0000-0002-6591-0123

DOI:

https://doi.org/10.24996/ijs.2026.67.1.27

Keywords:

Strongly nil-clean, Invo-clean, Invo-t-clean, Hosoya polynomial, Wiener index

Abstract

The definition of invo-clean rings is generalized to two involution clean rings. In this paper, we aimed to identify the structure with determined the basic properties of these rings. A ring is a two-involution clean if all elements are the sum of two involutions and idempotent elements. Additionally, the graph of two involution clean rings has been defined, and some properties of the new graph, such as: connected, the diameter, girth and others, have been proven.