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The time fractional diffusion equation with appropriate initial and boundary conditions in an n-dimensional whole-space and half-space is considered. Its solution has been obtained in terms of Green functions by Schneider and Wyss. For the problem in whole-space, an explicit representation of the Green functions can also be obtained. However, an explicit… (More)

- 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)

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 va-lencies.

- Fenjin Liu
- Ars Comb.
- 2015

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

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

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

- FENJIN LIU, QINGHAI LIU
- 2011

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

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

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