- explain why the dfs traversal runs in ( time on an -vertex simple graph that is represented with the adjacency matrix structure - in order to verify that all of its nontree edges are back edgesredraw the graph from figure so that the dfs tree edges are drawn with solid lines and oriented downwardas in standard portrayal of treeand with all nontree edges drawn using dashed lines - simple undirected graph is complete if it contains an edge between every pair of distinct vertices what does depth-first search tree of complete graph look liker- recalling the definition of complete graph from exercise - what does breadth-first search tree of complete graph look liker- let be an undirected graph whose vertices are the integers through and let the adjacent vertices of each vertex be given by the table belowvertex adjacent vertices ( ( ( ( ( ( ( ( assume thatin traversal of gthe adjacent vertices of given vertex are returned in the same order as they are listed in the table above draw give the sequence of vertices of visited using dfs traversal starting at vertex give the sequence of vertices visited using bfs traversal starting at vertex - draw the transitive closure of the directed graph shown in figure - if the vertices of the graph from figure are numbered as ( jfkv laxv miav bosv ordv sfov dfw)in what order would edges be added to the transitive closure during the floyd-warshall algorithmr- how many edges are in the transitive closure of graph that consists of simple directed path of verticesr- given an -node complete binary tree rooted at given positionconhaving the nodes of as its vertices for each sider directed graph from the parent to the parent-child pair in create directed edge in child show that the transitive closure of has ( log nedges