KnowraConnected graphLinked fromLinked fromThe 11 pages that link to Connected graph, each with the reason it gives.All 11Broader topic 1Related 8Narrower topic 1Compared with 1Graph theoryRelated: Connectivity asks whether the graph remains traversable between all its vertices.Complete graphCompared with: Connectivity requires routes between pairs, not direct edges between every pair.Graph (discrete mathematics)Broader topic: Connectivity asks whether edge chains link all vertices into one component.Tree (graph theory)Related: Connectivity supplies the reachability required by the definition of a tree.Path graphRelated: Every path graph is connected because its consecutive edges link all vertices.Spanning treeRelated: A graph has a spanning tree exactly when it is connected.Menger's theoremRelated: Removing a separator is defined by the loss of connection between endpoints.Hamiltonian pathRelated: A Hamiltonian path implies connectivity, but connectivity alone does not guarantee one.Brooks' theoremRelated: Connectedness is an explicit condition in Brooks' theorem.Lovász conjectureNarrower topic: The conjecture excludes disconnected graphs, where one spanning path cannot exist.Robbins' theoremRelated: Connectedness is the theorem’s starting condition before edges receive directions.