An Application of Hoffman Graphs for Spectral Characterizations of Graphs

Qianqian Yang, Aida Abiad, Jack H. Koolen

Abstract


In 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.

Keywords


Hoffman graph, Graph eigenvalue, Interlacing, Walk-regular, Spectral characterization

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