$(22\mathrm{.}5$ pts$.)$ Circle and fill T or F for each of the following statements to indicate whether

the statement is true or false, respectively. If the statement is wrong, explain why.

TF The possible maximum number of edges in a graph with $n$ nodes is $n^3.$

TF The heights of any two siblings in a binary heap differ by at least $1.$

TF Any subtree of an AVL tree is always itself an AVL tree

TF An AVL tree is always the same after deletion and then insertion the same node

TF A tree is a graph that may have cycle

TF Adjacency list representation of graphs is less efficient than adjacency matrix

representation for dense graphs.

TF Recursive function calls use queue

TF A binary heap is also an AVL tree

TF The length of a path is the number of edges on that path

TF The possible maximum number of nodes on level $k$ of a binary tree is $2k$

TF Depth of a node in a tree is the number of edges on the path from the node to the

deepest leaf

TF Every node in a tree has at most $2$ children.

TF Linked list nodes are normally stored contiguously in memory.

TF A stack is a linked$-$list that can be accessed from either end.

TF Push is used to place elements on the bottom of a stack and pop is used to remove

elements from the top of a stack.