On the Radius and the Relation Between the Total Graph of a Commutative Ring and Its Extensions

Zoran Pucanović, Zoran Petrović

We discuss the determination of the radius of the total graph of a commutative ring $R$ in the case when this graph is connected. Typical extensions such as polynomial rings, formal power series, idealization of the $R$-module $M$ and relations between the total graph of the ring $R$ and its extensions are also dealt with.