arXiv subjects
Publications and source records attributed to Alexander D. Mednykh.
We present a construction of Neumaier graphs with nexus 1, which generalises two known constructions of Neumaier graphs. We also use W. Wang, L. Qiu, and Y. Hu switching to show that we construct cospectral Neumaier graphs. Finally, we show that several small strictly Neumaier graphs can be obtained from our construction, and give a geometric or algebraic description for each of these graphs.
We classify the normal subgroups K of the tetrahedral group Delta=[3,5,3]^+, the even subgroup of the Coxeter group Gamma=[3,5,3], with Delta/K isomorphic to a finite simple group L_2(q). We determine their normalisers N(K) in the isometry group of hyperbolic 3-space H^3, the isometry groups N(K)/K of the associated hyperbolic 3-manifolds H^3/K, and the symmetry groups N_{Gamma}(K)/K of the icosahedral tessellations of these manifolds, giving a detailed analysis of how L_2(q) acts on these tessellations.