Mister India

May 17th, 2015
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1. Determine if an undirected graph G = (V, E) is connected, where |V| = n and |E| = m. 2. Find all the cycles in an undirected graph G. 3. (Optional) Find all articulation points in G.

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Mister IndiaCycles in an Undirected Graph1. Determine if an undirected graph G = (V, E) is connected, where |V| = n and |E| = m. 2. Find all the cycles in an undirected graph G.3. (Optional) Find all articulation points in G.Terminology: Given an undirected graph, a depth-first search (DFS) algorithm constructs a directed tree from the root (first node in the V). If there exists a directed path in the tree from v to w, then v is an predecessor of w and w is a descendant of v. A node-node adjacency structure is an n n matrix such that entry aij = 1 if node i is adjacent to node j and 0 otherwise. A node-edge adjacency structure lists for each node, the nodes adjacent to it.ExampleLet V = {1,2,3,4} and E = {(1,2), (1,3), (2,3), (3,4)}. The node-node adjacency structure is 011010101101001021The node-edge adjacency structure is31: 2,32: 1,33: 1,2,44: 34Note that node 4 is called a leaf.(1 and 2) Depth-first search (DFS) can be used to solved all three problems. It is usually assumed that the graph data structure is of the type node-edge adjacency instead of node-node adjacency. In the node-edge adjacency structure, the nodes are numbered from 1 to n. The node-i record lists the nodes adjacent to node i (connected to node i by an edge). DFS starts by setting node 1 as the current node.DFS iteration (i is the current node) If one or more nodes of the node-i record were not yet visited from i, let node j be the first node not visited. If node

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