An application of Hoffman graphs for spectral characterizations of graphs

Qianqian Yang; Aida Abiad; Jack H. Koolen

doi:10.37236/6428

An application of Hoffman graphs for spectral characterizations of graphs

Qianqian Yang
, Aida Abiad
, Jack H. Koolen

Research output: Contribution to journal › Article › Academic › peer-review

4 Citations (Scopus)

Abstract

In this paper, we present that the 2-clique extension of the (t+1) × (t+1)-grid is determined by its spectrum if t is large enough. By applying results of Gavrilyuk and Koolen, this implies that the Grassmann graph J₂(2D, D) is determined by its intersection array as a distance-regular graph if D is large enough. The main tool we are using is Hoffman graphs.

Original language	English
Article number	#P1.12
Journal	The Electronic Journal of Combinatorics
Volume	24
Issue number	1
DOIs	https://doi.org/10.37236/6428
Publication status	Published - 20 Jan 2017
Externally published	Yes

Funding

Supported by the National Natural Science Foundation of China (No.11671376 and No.11671376).

Keywords

Graph eigenvalue
Hoffman graph
Interlacing
Spectral characterizations
Walk-regular

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10.37236/6428

Cite this

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AU - Koolen, Jack H.

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AB - In this paper, we present that the 2-clique extension of the (t+1) × (t+1)-grid is determined by its spectrum if t is large enough. By applying results of Gavrilyuk and Koolen, this implies that the Grassmann graph J2(2D, D) is determined by its intersection array as a distance-regular graph if D is large enough. The main tool we are using is Hoffman graphs.

KW - Graph eigenvalue

KW - Hoffman graph

KW - Interlacing

KW - Spectral characterizations

KW - Walk-regular

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DO - 10.37236/6428

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ER -

An application of Hoffman graphs for spectral characterizations of graphs

Abstract

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Keywords

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