  A graph $G = (V,E)$ can be described by the characteristic function of the
edge set $\chi_E$ which maps a pair of binary encoded nodes to 1 iff the nodes
are adjacent. Using \emph{Ordered Binary Decision Diagrams} (OBDDs) to store
$\chi_E$ can lead to a (hopefully) compact representation. Given the OBDD as an
input, symbolic/implicit OBDD-based graph algorithms can solve optimization
problems by mainly using functional operations, e.g. quantification or binary
synthesis. While the OBDD representation size can not be small in general, it
can be provable small for special graph classes and then also lead to fast
algorithms. In this paper, we show that the OBDD size of unit interval graphs
is $O(\ | V \ | /\log \ | V \ |)$ and the OBDD size of interval graphs is $O(\
| V \ | \log \ | V \ |)$ which both improve a known result from Nunkesser and
Woelfel (2009). Furthermore, we can show that using our variable order and node
labeling for interval graphs the worst-case OBDD size is $\Omega(\ | V \ | \log
\ | V \ |)$. We use the structure of the adjacency matrices to prove these
bounds. This method may be of independent interest and can be applied to other
graph classes. We also develop a maximum matching algorithm on unit interval
graphs using $O(\log \ | V \ |)$ operations and a coloring algorithm for unit
and general intervals graphs using $O(\log^2 \ | V \ |)$ operations and
evaluate the algorithms empirically.
