Geodesic
An application of Hoffman graphs for spectral characterizations of graphs
Qianqian Yang1 ; Aida Abiad2 ; Jack H. Koolen1
1University of Science and Technology of China
2Maastricht University
The electronic journal of combinatorics, Tome 24 (2017) no. 1
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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.
DOI : 10.37236/6428
Classification : 05C50
Mots-clés : Hoffman graph, graph eigenvalue, interlacing, walk-regular graph, spectral characterization

Qianqian Yang  1   ; Aida Abiad  2   ; Jack H. Koolen  1

1 University of Science and Technology of China
2 Maastricht University 
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     title = {An application of {Hoffman} graphs for spectral characterizations of graphs},
     journal = {The electronic journal of combinatorics},
     year = {2017},
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     number = {1},
     doi = {10.37236/6428},
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Qianqian Yang; Aida Abiad; Jack H. Koolen. An application of Hoffman graphs for spectral characterizations of graphs. The electronic journal of combinatorics, Tome 24 (2017) no. 1. doi: 10.37236/6428

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