Consider the following graph: ![0 (graph_1.-png) 1. Write down the adjacency matrix and adjacency lists specifying this graph. (Assume that the matrix rows and columns and vertices in the adjacency lists follow in the alphabetical order of the vertex labels.) 2. Starting at vertex `a' order, traverse the graph by depth-first search and construct the corresponding depth-first search tree. Give the order in which the vertices were reached for the first time (pushed onto the traversal stack) and the order in which the vertices became dead ends (popped off the stack). and resolving ties by the vertex alphabetical

How many entries would the adjacency list representation for the following graph contain? (Assume that the array slots for each vertex count as one entry, and the linked list nodes for edges each count as one entry as well.) D B E A F G

4-Clique Problem The clique problem is to find cliques in a graph. A clique is a set of vertices that are all adjacent - connected - to each other. A 4-clique is a set of 4 vertices that are all connected to each other. So in this example of the 4-Clique Problem, we have a 7-vertex graph. A brute-force algorithm has searched every possible combination of 4 vertices and found a set that forms a clique: https://en.wikipedia.org/wiki/Clique_problem   You should read the Wikipedia page for the Clique Problem (and then read wider if need be) if you need to understand more about it. Note that the Clique Problem is NP-Complete and therefore when the graph size is large a deterministic search is impractical. That makes it an ideal candidate for an evolutionary search. For this assignment you must suppose that you have been tasked to implement the 4-clique problem as an evolutionary algorithm for any graph with any number of vertices (an n-vertex graph). The algorithm succeeds if it finds a…

Given the following graph: 15 5. 13 4 a 11 e 12, 3 10 f 1 Type the weight of each edge in the order in which they will be selected when using Kruskal's algorithm to create a minimum spanning tree. Be sure to separate the weights using a single space. Do not separate them with commas or any other characters.