# Given a graph G with only positive-weight edges and all edge weights are distinct, for vertices… 1 answer below »

Given a graph G with only positive-weight edges and all edge weights are

distinct, for vertices u and v, there must be a unique shortest path from u to v.

f. If a tree does not have the Binary-Search-Tree property, then any rotations will

result in a tree that also does not have this property.

g. If we have a min heap of 7 unique integers, then using a preorder traversal will

never print the values of the heap in increasing order.

h. The edge with the second smallest weight in a connected undirected graph with

distinct-weight edges must be part of any minimum spanning tree of the graph.

You can assume that there is at most one edge between any pair of vertices.

i. Given a directed weighted graph G, and two vertices u and v in G. The shortest

path from u to v remains unchanged if we add 330 to all edge weights. You can

assume that there is a unique shortest path from u to v before we add the

weights.

j. If an undirected graph with n vertices has k connected components, then it

must have at least n – k edges.