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- Hall–Janko_graph abstract "In the mathematical field of graph theory, the Hall–Janko graph, also known as the Hall-Janko-Wales graph, is a 36-regular undirected graph with 100 vertices and 1800 edges.It is a rank 3 strongly regular graph with parameters (100,36,14,12) and a maximum coclique of size 10. This parameter set is not unique, it is however uniquely determined by its parameters as a rank 3 graph. The Hall–Janko graph was originally constructed by D. Wales to establish the existence of the Hall-Janko group as an index 2 subgroup of its automorphism group. The Hall–Janko graph can be constructed out of objects in U3(3), the simple group of order 6048: In U3(3) there are 36 simple maximal subgroups of order 168. These are the vertices of a subgraph, the U3(3) graph. A 168-subgroup has 14 maximal subgroups of order 24, isomorphic to S4. Two 168-subgroups are called adjacent when they intersect in a 24-subgroup. The U3(3) graph is strongly regular, with parameters (36,14,4,6) There are 63 involutions (elements of order 2). A 168-subgroup contains 21 involutions, which are defined to be neighbors. Outside U3(3) let there be a 100th vertex C, whose neighbors are the 36 168-subgroups. A 168-subgroup then has 14 common neighbors with C and in all 1+14+21 neighbors. An involution is found in 12 of the 168-subgroups. C and an involution are non-adjacent, with 12 common neighbors. Two involutions are defined as adjacent when they generate a dihedral subgroup of order 8. An involution has 24 involutions as neighbors.The characteristic polynomial of the Hall–Janko graph is . Therefore the Hall–Janko graph is an integral graph: its spectrum consists entirely of integers.".
- Hall–Janko_graph thumbnail Hall_janko_graph.svg?width=300.
- Hall–Janko_graph wikiPageID "1110667".
- Hall–Janko_graph wikiPageRevisionID "551254834".
- Hall–Janko_graph chromaticNumber "10".
- Hall–Janko_graph diameter "2".
- Hall–Janko_graph edges "1800".
- Hall–Janko_graph girth "3".
- Hall–Janko_graph imageCaption "HJ as Foster graph plus Steiner system S .".
- Hall–Janko_graph name "Hall–Janko graph".
- Hall–Janko_graph namesake Marshall_Hall_(mathematician).
- Hall–Janko_graph namesake Zvonimir_Janko.
- Hall–Janko_graph properties Cayley_graph.
- Hall–Janko_graph properties Eulerian_path.
- Hall–Janko_graph properties Hamiltonian_path.
- Hall–Janko_graph properties Integral_graph.
- Hall–Janko_graph properties Strongly_regular_graph.
- Hall–Janko_graph properties Vertex-transitive_graph.
- Hall–Janko_graph radius "2".
- Hall–Janko_graph vertices "100".
- Hall–Janko_graph subject Category:Group_theory.
- Hall–Janko_graph subject Category:Individual_graphs.
- Hall–Janko_graph subject Category:Regular_graphs.
- Hall–Janko_graph comment "In the mathematical field of graph theory, the Hall–Janko graph, also known as the Hall-Janko-Wales graph, is a 36-regular undirected graph with 100 vertices and 1800 edges.It is a rank 3 strongly regular graph with parameters (100,36,14,12) and a maximum coclique of size 10. This parameter set is not unique, it is however uniquely determined by its parameters as a rank 3 graph. The Hall–Janko graph was originally constructed by D.".
- Hall–Janko_graph label "Graphe de Hall-Janko".
- Hall–Janko_graph label "Hall–Janko graph".
- Hall–Janko_graph sameAs Hall%E2%80%93Janko_graph.
- Hall–Janko_graph sameAs Graphe_de_Hall-Janko.
- Hall–Janko_graph sameAs Q260174.
- Hall–Janko_graph sameAs Q260174.
- Hall–Janko_graph wasDerivedFrom Hall–Janko_graph?oldid=551254834.
- Hall–Janko_graph depiction Hall_janko_graph.svg.