Question $7(10$ pts$)$

True$/$False$?$

$1)$ If no path exists between $2$ vertices in a weighted and undirected graph, then no minimum spanning tree exists for the graph.

$2)$ A minimum spanning tree is a set of vertices.

$3)$ The "minimum" in "minimum spanning tree" refers to the sum of edge weights.

$4)$ A minimum spanning tree can only be built for an undirected graph.

Question $8(1$ pt$)$

Minimum spanning tree $-$ critical thinking: True$/$False$?$

$1)$ The edge with the lowest weight will always be in the minimum spanning tree.

$2)$ The minimum spanning tree may contain all edges from the graph.

$3)$ Only $1$ minimum spanning tree exists for a graph that has no duplicate edge weights.

$4)$ The edges from any minimum spanning tree can be used to create a path that goes through all vertices in the graph without ever encountering the same vertex twice.