graphs some typical graph representations are vertex list with adjacency informationan edge listor an adjacency matrix review questions answer these short answermultiple choiceand true/false questions to test your mastery of the in the definition of graphg (ve)what does the and the stand for what is the difference in the definition of in directed and undirected graphs in depth first searchwhat is the purpose of the visited set how is backtracking accomplished in depth first search of graphexplain how the backtracking happens what is path in graph and how does that differ from cycle what is treefor the graph in fig provide three trees that include the vertices and why does kruskal' algorithm never make mistake when selecting edges for the minimum weighted spanning tree why does dijkstra' algorithm never make mistake when computing the cost of paths to vertices what graph representation is best for kruskal' algorithmwhy why is the previous vertex stored by dijkstra' algorithmwhat purpose does the previous vertex have and why is it stored programming problems write program to find path between vertex and in the graph shown in fig be sure to print the path ( the sequence of verticesthat must be traversed in the path between the two vertices an xml file describing this graph can be found on the text website modify the first problem to find the shortest path between vertices and in terms of the number of edges traversed in other wordsignore the weights in this problem use breadth first search to find this solution write the code and perform dijkstra' algorithm on the graph in fig to find the minimum cost of visiting all other vertices from vertex of the graph write the code and perform kruskal' algorithm on either the directed graph in fig or the undirected example found in the xml files for both graphs can be found on the text website not every graph must be represented explicitly sometimes it is just as easy to write function that given vertexwill compute the vertices that are adjacent to it (that have edges between themfor instanceconsider the water bucket this copy belongs to 'acha