Abstract.In [2l, L. Chihara proved that many infinite families of classical distance-regular graphs have no nontrivial perfect codes, including the Grassman graphs and the bilinear forms graphs. Here, we present a new proof of her result for these two families using Delsarte's anticode condition [3]. The technique is an extension of an approach taken by C. Roos [6] in the study of perfect codes in the Johnson graphs.

No abstract

No abstract

Topological materials support robust quantum states. Recent experiments demonstrate the topologically induced spin-polarized Majorana-type end state and boundary state in Stype armchair graphene nanoribbons (A-GNRs). Here, we report the topologically induced spin-polarized interface states in the topological GNRs constructed by alternating trivial armchair-edged GNR and nontrivial cove-edged GNR (C-GNR) segments (A/C-GNRs) from first-principles calculations. Distinct from spinpolarized states observed in zigzag GNRs, chiral GNRs, and Stype A-GNRs, the spin-polarized states in A/C-GNRs have the net spin distributed on the boundary region with antiferromagnetic coupling between opposite interfaces, the calculated magnetic moment is about 2 μ B in integer, and the Curie temperature is high to 350 K. The universality has been evaluated. It is revealed that the topological phase is responsible for such interface magnetism. Hence, our findings provide obvious evidence for topologically induced spin-polarized interface states, which can enrich the knowledge of GNR-based magnetism and have promising applications featured by the robustness.

No abstract