$1-5$ Consider a max heap $T$ with $30$ nodes represented by an array as discussed in class. How many swapping do we need if a value smaller than all existing values is inserted? Where will the new value be placed? Answer the same questions above when a value larger than all existing values is inserted.

$1-6$ Given an undirected graph $G$ which has exactly two connected components $H1$ and $H2.$ What is the relationship between the set of vertices $V1$ of $H1$ and the set of vertices $V2$ of $H2?$ Let $V$ be the set of vertices of $G.$ What is the relationship between $V,V1$ and $V2?$ Briefly explain you answers.

$($ANS$)$

$1-7$ Given a biconnected graph $G,$ will the graph be connected after the removal of an edge? Will $G$ be connected after the removal of a vertex? Consider all possible cases and briefly explain your answer.