An Application of Hoffman Graphs for Spectral Characterizations of Graphs
Keywords: Hoffman graph, Graph eigenvalue, Interlacing, Walk-regular, Spectral characterization
AbstractIn this paper, we present the first application of Hoffman graphs for spectral characterizations of graphs. In particular, we show that the 2-clique extension of the $(t+1)\times (t+1)$-grid is determined by its spectrum when $t$ is large enough. This result will help to show that the Grassmann graph $J_2(2D,D)$ is determined by its intersection numbers as a distance regular graph, if $D$ is large enough.