The total graph of a finite commutative ring

ISSN: 1300-0098
Yayın Aralığı: Yılda 6 Sayı
Yayıncı: TÜBİTAK

Let R be a commutative ring with Z(R), its set of zero-divisors and \mbox{Reg}(R), its set of regular elements. Total graph of R, denoted by T(G(R)), is the graph with all elements of R as vertices, and two distinct vertices x,y \in R, are adjacent in T(G(R)) if and only if x+y \in Z(R). In this paper, some properties of T(G(R)) have been investigated, where R is a finite commutative ring and a new upper bound for vertex-connectivity has been obtained in this case. Also, we have proved that the edge-connectivity of T(G(R)) coincides with the minimum degree if and only if R is a finite commutative ring such that Z(R) is not an ideal in R.

Anahtar Kelimeler:

Commutative rings, total graph, regular elements, zero-divisors

The total graph of a finite commutative ring

Keywords:

Commutative rings, total graph, regular elements, zero-divisors,

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