write program to find the strongly connected components in digraph give an algorithm that finds the strongly connected components in only one depthfirst search use an algorithm similar to the biconnectivity algorithm the biconnected components of graphgis partition of the edges into sets such that the graph formed by each set of edges is biconnected modify the algorithm in figure to find the biconnected components instead of the articulation points suppose we perform breadth-first search of an undirected graph and build breadth-first spanning tree show that all edges in the tree are either tree edges or cross edges give an algorithm to find in an undirected (connectedgraph path that goes through every edge exactly once in each direction write program to find an euler circuit in graph if one exists write program to find an euler tour in graph if one exists an euler circuit in directed graph is cycle in which every edge is visited exactly once prove that directed graph has an euler circuit if and only if it is strongly connected and every vertex has equal indegree and outdegree give linear-time algorithm to find an euler circuit in directed graph where one exists consider the following solution to the euler circuit problemassume that the graph is biconnected perform depth-first searchtaking back edges only as last resort if the graph is not biconnectedapply the algorithm recursively on the biconnected components does this algorithm workb suppose that when taking back edgeswe take the back edge to the nearest ancestor does the algorithm work planar graph is graph that can be drawn in plane without any two edges intersecting show that neither of the graphs in figure is planar show that in planar graphthere must exist some vertex which is connected to no more than five nodes  show that in planar graph| < | figure graph used in exercise