M22 graph

The M22 graph, also called the Mesner graph,[1][2][3] is the unique strongly regular graph with parameters (77, 16, 0, 4).[4] It is constructed from the Steiner system (3, 6, 22) by representing its 77 blocks as vertices and joining two vertices iff they have no terms in common or by deleting a vertex and its neighbors from the Higman–Sims graph.[5][6]

M22 graph, Mesner graph[1][2][3]
Named afterMathieu group M22, Dale M. Mesner
Vertices77
Edges616
Table of graphs and parameters

It is one of seven known triangle-free strongly regular graphs.[7] Its graph spectrum is (−6)21255161,[5] and its automorphism group is the Mathieu group M22.[4]

See also

References
  1. "Mesner graph with parameters (77,16,0,4). The automorphism group is of order 887040 and is isomorphic to the stabilizer of a point in the automorphism group of NL2(10)"
  2. Slide 5 list of triangle-free SRGs says "Mesner graph"
  3. Section 3.2.6 Mesner graph
  4. Brouwer, Andries E. “M22 Graph.” Technische Universiteit Eindhoven, http://www.win.tue.nl/~aeb/graphs/M22.html. Accessed 29 May 2018.
  5. Weisstein, Eric W. “M22 Graph.” MathWorld, http://mathworld.wolfram.com/M22Graph.html. Accessed 29 May 2018.
  6. Vis, Timothy. “The Higman–Sims Graph.” University of Colorado Denver, http://math.ucdenver.edu/~wcherowi/courses/m6023/tim.pdf. Accessed 29 May 2018.
  7. Weisstein, Eric W. “Strongly Regular Graph.” From Wolfram MathWorld, mathworld.wolfram.com/StronglyRegularGraph.html.
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