Unitary Invertible Graphs of Finite Rings

Abstract

Let R be a finite commutative ring with unity. In this paper, we consider set of additive and mutual additive inverses of group units of R and obtain interrelations between them. In general φ(Zn) is even, however we demonstrate that φ(R) is odd for any finite commutative ring with unity of Char(R) ≠ 2. Further, we present unitary invertible graph related with self and mutual additive inverses of group units. At long last, we establish a formula for counting the total number of basic and non-basic triangles in the unitary invertible graph.

Keywords

• finite commutative rings
• additive and mutual additive inverses
• euler-function
• unitary invertible graphs
• basic and non-basic triangles
• 11g15
• 11t30
• 05c30