An Application of Hoffman Graphs for Spectral Characterizations of Graphs
An Application of Hoffman Graphs for Spectral Characterizations of Graphs
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DOI：
10.37236/6428
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发表时间：
2016-08
期刊：
影响因子：
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通讯作者：
Qianqian Yang;A. Abiad;J. Koolen
中科院分区：
文献类型：
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作者：
Qianqian Yang;A. Abiad;J. Koolen
在本文中，我们提出了霍夫曼图在图的谱表征中的第一个应用。特别地，我们证明了$(t+1)\乘以（t+1）$-网格的$2$-团扩展是由$t$足够大时它的谱决定的。这一结果有助于证明，当D足够大时，Grassmann图J_2(2D，D)$是由它的相交数决定的距离正则图。
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.