Hoffman-Singleton Graph
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منابع مشابه
On the Graphs of Hoffman-Singleton and Higman-Sims
We propose a new elementary definition of the Higman-Sims graph in which the 100 vertices are parametrised with Z4 × Z5 × Z5 and adjacencies are described by linear and quadratic equations. This definition extends Robertson’s pentagonpentagram definition of the Hoffman-Singleton graph and is obtained by studying maximum cocliques of the Hoffman-Singleton graph in Robertson’s parametrisation. Th...
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We describe the Hoffman-Singleton graph geometrically, showing that it is closely related to the incidence graph of the affine plane over Z5. This allows us to construct all automorphisms of the graph.
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In this paper, we give a new construction of the McLaughlin graph from the Hoffman-Singleton graph.
متن کاملThe graphs of Hoffman-Singleton, Higman-Sims, McLaughlin and the Hermite curve of degree 6 in characteristic 5
We construct the graphs of Hoffman-Singleton, Higman-Sims and McLaughlin from certain relations on the set of non-singular conics totally tangent to the Hermitian curve of degree 6 in characteristic 5. We then interpret this geometric construction in terms of the subgroup structure of the automorphism group of this Hermitian curve.
متن کاملBinary codes derived from the Hoffman-Singleton and Higman-Sims graphs
Some binary linear codes of length 50 and 100 are constructed using the adjacency matrices of the Hooman-Singleton graph and the Higman-Sims graph. Some of the codes are optimal or nearly optimal for the given length and dimension. The dual codes admit majority logic decoding.
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تاریخ انتشار 2007