True or false: A max flow of a graph is always the sum of a subset of its edges

What is the maximum number of edges that can be present in a graph, that has 10 vertices, and has a valid vertex coloring with only 3 colors?

The popular ways to traverse a graph are   a. depth-first traversal   b. binary traversal   c. breadth first traversal   d. linear traversal   e. quadratic traversal

Explain how one can check a graph’s acyclicity by using breadth-first search.

If there is a route from each vertex to every other vertex in the graph, it is called a directed graph.

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…

Please do not give solution in image format thanku Design an algorithm which accepts a directed graph as input, and determines if there is a vertex within the graph from which all other vertices are reachable. The algorithm should run in θ(|v| + |E|)

It's important to evaluate the merits and drawbacks of weighted graphs vs adjacency lists.

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

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