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 srg(100...

in the group of automorphisms of the Higman–Sims graph. The Higman–Sims graph has 100 nodes, so the Higman–Sims group HS is a transitive group of permutations...

like the odd graph O(4). A very similar construction from PG(3,2) is used to build the Higman–Sims graph, which has the Hoffman-Singleton graph as a subgraph...

The Brouwer–Haemers graph is an srg(81, 20, 1, 6). The Higman–Sims graph is an srg(100, 22, 0, 6). The Local McLaughlin graph is an srg(162, 56, 10...

graph Cameron graph Petersen graph Hall–Janko graph Hoffman–Singleton graph Higman–Sims graph Paley graph of order 13 Shrikhande graph Schläfli graph...

Examples of vector spaces Fano plane Frieze group Gray graph Hall–Janko graph Higman–Sims graph Hilbert matrix Illustration of a low-discrepancy sequence...

group: Order 2. Remarks: It acts as a rank 3 permutation group on the Higman Sims graph with 100 points, and is contained in Co2 and in Co3. Order: 27 ⋅ 36...

Higman he discovered the Higman–Sims group, one of the sporadic groups. The permutation group software developed by Sims also led to the proof of existence...

construction, one can embed the Gewirtz graph in the Higman–Sims graph. The characteristic polynomial of the Gewirtz graph is ( x − 10 ) ( x − 2 ) 35 ( x + 4...

homogeneous spaces, and automorphism groups of graphs, such as the Higman–Sims group and the Higman–Sims graph. The elements of the symmetric group on a set...

Nauru graph and the Desargues graph are integral. The Higman–Sims graph, the Hall–Janko graph, the Clebsch graph, the Hoffman–Singleton graph, the Shrikhande...

various individual (finite) graphs. The columns 'vertices', 'edges', 'radius', 'diameter', 'girth', 'P' (whether the graph is planar), χ (chromatic number)...

automorphism group is the Mathieu group M22. Cameron graph Higman–Sims graph Gewirtz graph "Mesner graph with parameters (77,16,0,4). The automorphism group...

presented groups that cannot be finitely presented. However a theorem of Graham Higman states that a finitely generated group has a recursive presentation if and...

stabilizer of a point has 3 orbits. The study of these groups was started by Higman (1964, 1971). Several of the sporadic simple groups were discovered as rank...

with the McLaughlin group McL (order 898,128,000) and .332 with the Higman–Sims group HS (order 44,352,000); both of these had recently been discovered...

general. That is, Higman's lemma does not carry over to infinite sequences. Better-quasi-orderings have been introduced to generalize Higman's lemma to sequences...

23 points, and also the point stabilizer of the rank 3 action of the Higman–Sims group on 100 = 1+22+77 points. The triple cover 3.M22 has a 6-dimensional...

The other non-abelian group of order 8 is the quaternion group Q8. The Higman–Sims asymptotic formula states that the number of isomorphism classes of groups...

abelian. If n is a higher power of a prime, then results of Graham Higman and Charles Sims give asymptotically correct estimates for the number of isomorphism...

Praeger, C. E.; Saxl, J.; Seitz, G. M. (1983). "On the Sims conjecture and distance transitive graphs". Bull. London Math. Soc. 15 (5): 499–506. doi:10.1112/blms/15...