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SELECTED TOPICS IN SPECTRAL GRAPH THEORY

Published online by Cambridge University Press:  17 February 2016

XIAOGANG LIU*
Affiliation:
School of Mathematics and Statistics, The University of Melbourne, Victoria 3010, Australia email [email protected]
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Abstract

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Type
Abstracts of Australasian PhD Theses
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

References

Cvetković, D., Rowlinson, P. and Simić, S. K., An Introduction to the Theory of Graph Spectra (Cambridge University Press, Cambridge, 2010).Google Scholar
Gutman, I., ‘The energy of a graph’, Ber. Math.-Statist. Sekt. Forsch. Graz 103(100–105) (1978), 122.Google Scholar
Gutman, I., ‘Hyperenergetic molecular graphs’, J. Serb. Chem. Soc. 64(3) (1999), 199205.Google Scholar
Hoory, S., Linial, N. and Wigderson, A., ‘Expander graphs and their applications’, Bull. Amer. Math. Soc. 43(4) (2006), 439561.Google Scholar
Liu, X. and Lu, P., ‘Spectra of subdivision-vertex and subdivision-edge neighbourhood coronae’, Linear Algebra Appl. 438(8) (2013), 35473559.CrossRefGoogle Scholar
Liu, X. and Lu, P., ‘Signless Laplacian spectral characterization of some joins’, Electron. J. Linear Algebra 30(1) (2015), 443454.Google Scholar
Liu, X. and Lu, P., ‘Laplacian spectral characterization of dumbbell graphs and theta graphs’, submitted.Google Scholar
Liu, X. and Zhou, S., ‘Spectral properties of unitary Cayley graphs of finite commutative rings’, Electron. J. Combin. 19(4) (2012), #P13.Google Scholar
Liu, X. and Zhou, S., ‘Spectra of the neighbourhood corona of two graphs’, Linear Multilinear Algebra 62(9) (2014), 12051219.CrossRefGoogle Scholar
Liu, X. and Zhou, S., ‘Spectral characterizations of propeller graphs’, Electron. J. Linear Algebra 27 (2014), 1938.Google Scholar
Liu, X. and Zhou, S., ‘Quadratic unitary Cayley graphs of finite commutative rings’, Linear Algebra Appl. 479 (2015), 7390.CrossRefGoogle Scholar
Lubotzky, A., ‘Expander graphs in pure and applied mathematics’, Bull. Amer. Math. Soc. 49(1) (2012), 113162.CrossRefGoogle Scholar
Lubotzky, A., Phillips, R. and Sarnak, P., ‘Ramanujan graphs’, Combinatorica 8(3) (1988), 261277.CrossRefGoogle Scholar
Ram Murty, M., ‘Ramanujan graphs’, J. Ramanujan Math. Soc. 18(1) (2003), 3352.Google Scholar