https://blogs.rameskum.com/tags/graphs/Recent content in Graphs on 1Stophttps://blogs.rameskum.com/images/og-default.pnghttps://blogs.rameskum.com/images/og-default.pngHugoen-usFri, 01 Mar 2024 09:00:00 +0000https://blogs.rameskum.com/posts/algorithms-graphs/Fri, 01 Mar 2024 09:00:00 +0000https://blogs.rameskum.com/posts/algorithms-graphs/<h2 id="undirected-graphs">Undirected Graphs</h2> <h3 id="some-problems">Some problems</h3> <ul> <li>Path</li> <li>Shortest path</li> <li>Cycle</li> <li>Ehler tour: A cycle that uses each edge excatly once.</li> <li>Hamilton tour: A cycle that uses each vertex exactly once <ul> <li>classical NP-complete problem.</li> </ul> </li> <li>Connectivity</li> <li>MST:</li> <li>Biconnectivity: A vertex whose removal disconnects the graph</li> <li>Planarity</li> <li>Graph isomorphism: Are two graphs identical? <ul> <li>No one knows so far. A lonstanding open problem</li> </ul> </li> </ul> <h3 id="representations">Representations</h3> <p>Real-world graphs tend to be <strong>sparse</strong> (huge number of vertices, small average vertex degree).</p>