design Highest-Degree First algorithm Python Implementation that uses the highest degree first heuristic as follows. We always select the highest degree uncolored vertex and color it with the minimum color that does not conflict with its neighbors

Python Graph Algorithms: Minimum Spanning Trees Suppose you are an engineer working on designing a road network for a new town. The town has many residential areas and commercial centers that need to be connected efficiently. You decided to represent the town as a connected, undirected graph where each vertex represents a location, and each edge represents a road connecting two locations. The weight of each edge represents the distance between the two locations. To ensure the road network is efficient, you need to find the minimum spanning tree of the graph. However, due to budget constraints, you can only construct roads with a maximum distance limit. You need to determine for how many pairs of locations, the minimum spanning tree of the graph remains the same when the maximum distance limit of a road is increased by 2 units. To solve this, you write a program that takes as input the number of locations, the number of roads, and the weight of each road. Your program will also receive…

in the C language create the smallest original degree last method for ordering of vertices in a graph.

2 F E 4 K5: the complete graph on 5 vertices. (ie. each vertex is connected to the other four vertices)

True or False: The sum of the degrees of the vertices of an undirected graph must be odd. True False

in C language implement a graph coloring method that assigns the minimum color to each vertex so it does conflict with vertices that have been colored (using adjacency list)

11. For the given graph below, use the depth-first search algorithm to visit the vertices and write the sequence of the visit. Start from the vertex "A". At any given vertex, you will visit first the unexplored vertex that has least alphabetical order. с G E F Answer the sequence of visiting the vertices: -_