TU Wien:Diskrete Mathematik für Informatik VO (Gittenberger)/Schriftliche Prüfung 2018-01-31

1. Given a graph and a flow (as weight matrix), find: value of the flow, augmenting paths (one with only forward edges, another with at least one backward edge), minimal cut, maximal flow.

2. Determine µ(0,1) for a given partial order (it was given as Hasse diagram).

3. Let R be an integral domain. Prove $(a)=\{ra\mid r\in R\}$.

4. Given a word $w\in \mathbb {Z} _{2}^{8}$ ($w=00011101$?). Is there a cyclic linear code $C\subseteq \mathbb {Z} _{2}^{8}$ such that $w\in C$?