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In this note, we consider connected graphs with exactly two main eigenvalues. We will give several constructions for them, and as a consequence we show a family of those graphs with an unbounded number of distinct valencies.

- Fenjin Liu, Wei Wang
- Electr. J. Comb.
- 2017

- Fenjin Liu, Qiongxiang Huang
- Ars Comb.
- 2013

- FENJIN LIU, QINGHAI LIU
- 2011

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 (fenjinliu@yahoo.cn, qiongxianghuang@sohu.com, liuqh506@163.com). Supported by NFSC Grant No. 10961023. Electronic Journal of Linear Algebra ISSN… (More)

- Xingming Tao, Qiongxiang Huang, Fenjin Liu
- Ars Comb.
- 2014

- Fenjin Liu, Wei Wang
- 2017

Two graphs G and H are called R-cospectral if A(G)+yJ and A(H)+yJ (where A(G), A(H) are the adjacency matrices of G and H, respectively, J is the all-one matrix) have the same spectrum for all y ∈ R. In this note, we give a necessary condition for having R-cospectral graphs. Further, we provide a sufficient condition ensuring only irrational orthogonal… (More)

- Fenjin Liu, Qiongxiang Huang, Xingming Tao
- Appl. Math. Lett.
- 2012

- Aygul Mamut, Qiongxiang Huang, Fenjin Liu
- Discrete Applied Mathematics
- 2009

- Fenjin Liu
- Ars Comb.
- 2015

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