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SPECTRALCHARACTERIZATIONOF † -SHAPETREES ELA

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ELA

SPECTRAL CHARACTERIZATION OF † -SHAPE TREES

∗

FENJIN LIU†, QIONGXIANG HUANG†, ANDQINGHAI LIU†

Abstract. The†-shape tree is the coalescence of the starK1,4 and the pathPn−4with respect to two pendent vertices. In this paper, it is showed that the †-shape tree is determined by its adjacency spectrum if and only ifn6= 2k+ 9 (k= 0,1, . . .). Furthermore, all the cospectral mates of the†-shape tree are found whenn= 2k+ 9.

Key words. †-shape tree, Adjacency spectrum, Spectral characterization, Cospectral graphs.

AMS subject classifications. 05C50.

∗Received by the editors on January 11, 2011. Accepted for publication on July 10, 2011. Handling Editor: Leslie Hogben.

†College of Mathematics and System Science, Xinjiang University, Urumqi, 830046, P.R. China ([email protected], [email protected], [email protected]). Supported by NFSC Grant No. 10961023.

Electronic Journal of Linear Algebra ISSN 1081-3810 A publication of the International Linear Algebra Society Volume 22, pp. 822-837, August 2011

http://math.technion.ac.il/iic/ela

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