Unitary Invertible Graphs of Finite Rings

Discussiones Mathematicae - General Algebra and Applications

卷:41

Sajana Shaik¹  Chalapathi Tekuri² 

[1] Department of Mathematics, P.R. Govt. Degree College (A), Kakinada, A.P., India;

[2] Department of Mathematics, Sree Vidyanikethan Engineering College, Tirupati, A.P., India;

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

DOI  :  10.7151/dmgaa.1350

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown