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- Higman–Sims_graph abstract "In mathematical graph theory, the Higman–Sims graph is a 22-regular undirected graph with 100 vertices and 1100 edges. It is the unique strongly regular graph with 100 vertices and valency 22, where no neighboring pair of vertices share a common neighbor and each non-neighboring pair of vertices share six common neighbors. It was first constructed by Mesner (1956) and rediscovered in 1968 by Donald G. Higman and Charles C. Sims as a way to define the Higman–Sims group, and that group is a subgroup of index two in the group of automorphisms of the Higman–Sims graph.Construction begins with the M22 graph, whose 77 vertices are the blocks of the S(3,6,22) Steiner system W22. Adjacent vertices are defined to be disjoint blocks. This graph is strongly regular; any vertex has 16 neighbors, any 2 adjacent vertices have no common neighbors, and any 2 non-adjacent vertices have 4 common neighbors. This graph has M22:2 as its automorphism group, M22 being a Mathieu group.The Higman–Sims graph is then formed by appending the 22 points of W22 and a 100th vertex C. The neighbors of C are defined to be those 22 points. A point adjacent to a block is defined to be one that is included.A Higman–Sims graph can be partitioned into two copies of the Hoffman–Singleton graph in 352 ways.".
- Higman–Sims_graph thumbnail Higman_Sims_Graph.svg?width=300.
- Higman–Sims_graph wikiPageID "1110499".
- Higman–Sims_graph wikiPageRevisionID "572650660".
- Higman–Sims_graph automorphisms "88704000".
- Higman–Sims_graph diameter "2".
- Higman–Sims_graph edges "1100".
- Higman–Sims_graph girth "4".
- Higman–Sims_graph imageCaption "Drawing based on Paul R. Hafner's construction.".
- Higman–Sims_graph name "Higman–Sims graph".
- Higman–Sims_graph namesake Charles_Sims_(mathematician).
- Higman–Sims_graph namesake Donald_G._Higman.
- Higman–Sims_graph properties Edge-transitive_graph.
- Higman–Sims_graph properties Eulerian_path.
- Higman–Sims_graph properties Hamiltonian_path.
- Higman–Sims_graph properties Strongly_regular_graph.
- Higman–Sims_graph radius "2".
- Higman–Sims_graph vertices "100".
- Higman–Sims_graph subject Category:Group_theory.
- Higman–Sims_graph subject Category:Individual_graphs.
- Higman–Sims_graph subject Category:Regular_graphs.
- Higman–Sims_graph comment "In mathematical graph theory, the Higman–Sims graph is a 22-regular undirected graph with 100 vertices and 1100 edges. It is the unique strongly regular graph with 100 vertices and valency 22, where no neighboring pair of vertices share a common neighbor and each non-neighboring pair of vertices share six common neighbors. It was first constructed by Mesner (1956) and rediscovered in 1968 by Donald G. Higman and Charles C.".
- Higman–Sims_graph label "Grafo de Higman-Sims".
- Higman–Sims_graph label "Graphe de Higman-Sims".
- Higman–Sims_graph label "Higman–Sims graph".
- Higman–Sims_graph sameAs Higman%E2%80%93Sims_graph.
- Higman–Sims_graph sameAs Graphe_de_Higman-Sims.
- Higman–Sims_graph sameAs Grafo_de_Higman-Sims.
- Higman–Sims_graph sameAs Q3115511.
- Higman–Sims_graph sameAs Q3115511.
- Higman–Sims_graph wasDerivedFrom Higman–Sims_graph?oldid=572650660.
- Higman–Sims_graph depiction Higman_Sims_Graph.svg.
