Please help... Adding one more vertices... highlighted with with bold... Let A, B, C, D be the vertices of a square with side length 100. If we want to create a minimum-weight spanning tree to connect these four vertices, clearly this spanning tree would have total weight 300 (e.g. we can connect AB, BC, and CD). But what if we are able to add extra vertices inside the square, and use these additional vertices in constructing our spanning tree? Would the minimum-weight spanning tree have total weight less than 300? And if so, where should these additional vertices be placed to minimize the total weight?

Suppose we have a community of n people. We can create a directed graph from this community as follows: the vertices are people, and there is a directed edge from person A to person B if A would forward a rumor to B. Assume that if there is an edge from A to B, then A will always forward any rumor they hear to B. Notice that this relationship isn’t symmetric: A might gossip to B but not vice versa. Suppose there are m directed edges total, so G = (V, E) is a graph with n vertices and m edges.Define a person P to be influential if for all other people A in the community, there is a directed path from P to A in G. Thus, if you tell a rumor to an influential person P , eventually the rumor will reach everybody. You have a rumor that you’d like to spread, but you don’t have time to tell more than one person, so you’d like to find an influential person to tell the rumor to. In the following questions, assume that G is the directed graph representing the community, and that you have access…

4. For the graph below: a. A snow plow starts at vertex 0 and must return to vertex 0 using a route which visits each edge at least once and repeats a minimum number of edges. Find such a route and how many repeated edges does it have? Assume that the edges all have the length, say length 1.

Need help with these true or false questions.