graph algorithms figure graph with articulation points and unaffectedexceptof courseat the down computer similarlyif mass transit system is biconnectedusers always have an alternate route should some terminal be disrupted if graph is not biconnectedthe vertices whose removal would disconnect the graph are known as articulation points these nodes are critical in many applications the graph in figure is not biconnectedc and are articulation points the removal of would disconnect gand the removal of would disconnect and ffrom the rest of the graph depth-first search provides linear-time algorithm to find all articulation points in connected graph firststarting at any vertexwe perform depth-first search and number the nodes as they are visited for each vertexvwe call this preorder number num(vthenfor every vertexvin the depth-first search spanning treewe compute the lowestnumbered vertexwhich we call low( )that is reachable from by taking zero or more tree edges and then possibly one back edge (in that orderthe depth-first search tree in figure shows the preorder number firstand then the lowest-numbered vertex reachable under the rule described above the lowest-numbered vertex reachable by aband is vertex ( )because they can all take tree edges to and then one back edge back to we can efficiently compute low by performing postorder traversal of the depth-first spanning tree by the definition of lowlow(vis the minimum of num( the lowest num(wamong all back edges (vw the lowest low(wamong all tree edges (vwthe first condition is the option of taking no edgesthe second way is to choose no tree edges and back edgeand the third way is to choose some tree edges and possibly