What is $\tau(A)$ of components of $G \backslash A$, where $A \subseteq V$? A graph is $t$-tough if for all cutsets $A$ we have :
definition of t-tough can be found here 
http://personal.stevens.edu/~dbauer/pdf/dmn04f6.pdf
Now I am reading a paper which author defines t-tough graph in other terms:
Link to the paper: 
http://www.sciencedirect.com/science/article/pii/S0012365X09002775
"Graph $G$ is $\alpha$-tough if the number $\tau(A)$ of components of $G\backslash A$ is at most max$\{1, |A|/\alpha\}$ for every non empty set A of vertices."
The question is : What is $\tau (A)$??

From the context you provided, it seems that the definition of $\tau(A)$ is given in the sentence you quote:
$\tau(A)$ is the number of connected components of the graph $G\setminus A$, obtained by removing from $G$ a subset $A$ of its vertices.
