## On the radius and the relation between the total graph of a commutative ring and its extensions.(English)Zbl 1299.13010

Summary: 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.

### MSC:

 13A99 General commutative ring theory

zero-divisor
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