Write an algorithm in pseudo code that, for a given graph, outputs its cycle or a message that the graph is acyclic.

Consider a graph with five nodes labeled A, B, C, D, and E. Let's say we have the following edges with their weights: A to B with weight 3 A to C with weight 1 B to C with weight 2 B to D with weight 1 C to E with weight 4 D to E with weight 2 a. Find the shortest path from A to E using Dijkstra's algorithm. (Draw the finished shortest path) b. Use Prim to find the MST (Draw the finished MST) c. Use Kruskal to find the MST (Draw the finished MST) d. What's the difference between Prim and Kruskal algorithms? Do they always have the same result? Why or why not.

given an ordering of vertices in a graph, implement a minimum coloring of the vertices in C language. (using adjacency list not matrix)he output would be Vertex 1->2 Color->Red, Vertex 2->3 Color ->Blue with an input of The input would be a string of vertex like 2358691.

Consider the following graph: a Specify a simple cycle. Use only lower case letters. If the graph has any cycles which are not simple and which have no repeated edges, specify one. If there are none enter none Use only lower case letters.