Given an undirected graph with $6$ edges, $1$ vertex of degree $3$ and $1$ vertex of degree $5,$ and the rest are vertices of degree $2,$ how many vertices does the graph have?

$2.$Draw all the non$-$isomorphic undirected simple graphs with $5$ vertices and $3$ edges.

$.$Find the vertex connectivity $$ and the edge connectivity $$ of the Petersen graph.