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- Panconnectivity abstract "In graph theory, a panconnected graph is an undirected graph in which, for every two vertices s and t, there exist paths from s to t of every possible length from the distance d(s,t) up to n − 1, where n is the number of vertices in the graph. The concept of panconnectivity was introduced in 1975 by Yousef Alavi and James E. Williamson.Panconnected graphs are necessarily pancyclic: if uv is an edge, then it belongs to a cycle of every possible length, and therefore the graph contains a cycle of every possible length.Panconnected graphs and are also a generalization of Hamiltonian-connected graphs (graphs that have a Hamiltonian path connecting every pair of vertices).Several classes of graphs are known to be panconnected:If G has a Hamiltonian cycle, then the square of G (the graph on the same vertex set that has an edge between every two vertices whose distance in G is at most two) is panconnected.If G is any connected graph, then the cube of G (the graph on the same vertex set that has an edge between every two vertices whose distance in G is at most three) is panconnected.If every vertex in an n-vertex graph has degree at least n/2 + 1, then the graph is panconnected.If an n-vertex graph has at least (n − 1)(n − 2)/2 + 3 edges, then the graph is panconnected.↑ 1.0 1.1 1.2 ↑ 2.0 2.1".
- Panconnectivity wikiPageID "29341653".
- Panconnectivity wikiPageLength "2362".
- Panconnectivity wikiPageOutDegree "12".
- Panconnectivity wikiPageRevisionID "574580060".
- Panconnectivity wikiPageWikiLink Category:Graph_families.
- Panconnectivity wikiPageWikiLink Connected_graph.
- Panconnectivity wikiPageWikiLink Connectivity_(graph_theory).
- Panconnectivity wikiPageWikiLink Cycle_(graph_theory).
- Panconnectivity wikiPageWikiLink Edge_(graph_theory).
- Panconnectivity wikiPageWikiLink Graph_(mathematics).
- Panconnectivity wikiPageWikiLink Graph_theory.
- Panconnectivity wikiPageWikiLink Hamiltonian_cycle.
- Panconnectivity wikiPageWikiLink Hamiltonian_path.
- Panconnectivity wikiPageWikiLink Pancyclic_graph.
- Panconnectivity wikiPageWikiLink Path_(graph_theory).
- Panconnectivity wikiPageWikiLink Undirected_graph.
- Panconnectivity wikiPageWikiLink Vertex_(graph_theory).
- Panconnectivity wikiPageWikiLink Yousef_Alavi.
- Panconnectivity hasPhotoCollection Panconnectivity.
- Panconnectivity wikiPageUsesTemplate Template:Math.
- Panconnectivity wikiPageUsesTemplate Template:Mvar.
- Panconnectivity wikiPageUsesTemplate Template:Reflist.
- Panconnectivity subject Category:Graph_families.
- Panconnectivity hypernym Graph.
- Panconnectivity type Software.
- Panconnectivity type Graph.
- Panconnectivity comment "In graph theory, a panconnected graph is an undirected graph in which, for every two vertices s and t, there exist paths from s to t of every possible length from the distance d(s,t) up to n − 1, where n is the number of vertices in the graph. The concept of panconnectivity was introduced in 1975 by Yousef Alavi and James E.".
- Panconnectivity label "Panconnectivity".
- Panconnectivity sameAs m.0ds3k7_.
- Panconnectivity sameAs Q7130383.
- Panconnectivity sameAs Q7130383.
- Panconnectivity wasDerivedFrom Panconnectivity?oldid=574580060.
- Panconnectivity isPrimaryTopicOf Panconnectivity.