Question $2$: In an undirected graph G$($V$,$ E$)$ an independent set is a set I $$ V so

that for every a $=$ b$,$ a$,$ b in I, $($a$,$ b$)$ in E namely no two vertices in I are neighbors. A dominating set is a set S so that for every a $$ in S there exists a vertex b in S so that

$($a$,$ b$)$ in E$.$ Show that there is always an independent set that is also a dominating set.Give an algorithm that finds an independent set that is also a dominating set.

Remarks: All the graphs here are without self loops and parallel or anti$-$parallel edges.In all the algorithms, always explain their correctness and analyze their complexity. The complexity should be as small as possible. A correct algorithm with large complexity, may not good. You are not allowed to write programs but can write psudo code.