Two Involution Clean Rings with Applications in Graph Theory
Strongly nil-clean
Invo-clean
Invo-t-clean
Hosoya polynomial
Wiener index
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.