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An upper bound on the Laplacian spectral radius of the signed graphs

Hong-Hai LiJiong-Sheng Li — 2008

Discussiones Mathematicae Graph Theory

In this paper, we established a connection between the Laplacian eigenvalues of a signed graph and those of a mixed graph, gave a new upper bound for the largest Laplacian eigenvalue of a signed graph and characterized the extremal graph whose largest Laplacian eigenvalue achieved the upper bound. In addition, an example showed that the upper bound is the best in known upper bounds for some cases.

Entire functions that share values or small functions with their derivatives

Sheng LiZongsheng GaoJilong Zhang — 2012

Annales Polonici Mathematici

We investigate the uniqueness of entire functions sharing values or small functions with their derivatives. One of our results gives a necessary condition on the Nevanlinna deficiency of the entire function f sharing one nonzero finite value CM with its derivative f'. Some applications of this result are provided. Finally, we prove some further results on small function sharing.

Distribution of zeros and shared values of difference operators

Jilong ZhangZongsheng GaoSheng Li — 2011

Annales Polonici Mathematici

We investigate the distribution of zeros and shared values of the difference operator on meromorphic functions. In particular, we show that if f is a transcendental meromorphic function of finite order with a small number of poles, c is a non-zero complex constant such that Δ c k f 0 for n ≥ 2, and a is a small function with respect to f, then f Δ c k f equals a (≠ 0,∞) at infinitely many points. Uniqueness of difference polynomials with the same 1-points or fixed points is also proved.

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