Some properties of the Hoffman-Singleton graph

Hoffman-Singleton Graph

The Hoffman-Singleton Graph and its Automorphisms

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.

A construction of the McLaughlin graph from the Hoffman-Singleton graph

In this paper, we give a new construction of the McLaughlin graph from the Hoffman-Singleton graph.

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

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...