The study of strings is an important combinatorial field that precedes the
digital computer. Strings can be very long, trillions of letters, so it is
important to find compact representations. Here we first survey various forms
of one potential compaction methodology, the cover of a given string x,
initially proposed in a simple form in 1990, but increasingly of interest as
more sophisticated variants have been discovered. We then consider covering by
a seed; that is, a cover of a superstring of x. We conclude with many proposals
for research directions that could make significant contributions to string
processing in future.

The Knödel graph $W_{\Delta,n}$ is a $\Delta$-regular bipartition graph on
$n\ge 2^{\Delta}$ vertices and $n$ is an even integer. The vertices of
$W_{\Delta,n}$ are the pairs $(i,j)$ with $i=1,2$ and $0\le j\le n/2-1$. For
every $j$, $0\le j\le n/2-1$, there is an edge between vertex $(1, j)$ and
every vertex $(2,(j+2^k-1) \mod (n/2))$, for $k=0,1,\cdots,\Delta-1$. In this
paper we obtain some formulas for evaluating the distance of vertices of the
Knödel graph and by them, we provide the formula
$diam(W_{\Delta,n})=1+\lceil\frac{n-2}{2^{\Delta}-2}\rceil$ for the diameter of
$W_{\Delta,n}$, where $n\ge (2\Delta-5)(2^{\Delta}-2)+4$.