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Functions on adjacent vertex degrees of trees with given degree sequence

100%

Wang H.

Open Mathematics

2014

tom 12

nr 11

1656-1663

In this note we consider a discrete symmetric function f(x, y) where $$f(x,a) + f(y,b) \geqslant f(y,a) + f(x,b) for any x \geqslant y and a \geqslant b,$$ associated with the degrees of adjacent vertices in a tree. The extremal trees with respect to the corresponding graph invariant, defined as $$\sum\limits_{uv \in E(T)} {f(deg(u),deg(v))} ,$$ are characterized by the “greedy tree” and “alternating greedy tree”. This is achieved through simple generalizations of previously used ideas on similar questions. As special cases, the already known extremal structures of the Randic index follow as corollaries. The extremal structures for the relatively new sum-connectivity index and harmonic index also follow immediately, some of these extremal structures have not been identified in previous studies.

On meromorphic functions for sharing two sets and three sets inm-punctured complex plane

51%

Xu H.-Y., Zheng X.-M., Wang H.

Open Mathematics

2016

tom 14

nr 1

913-924

In this article, we study the uniqueness problem of meromorphic functions in m-punctured complex plane Ω and obtain that there exist two sets S1, S2 with ♯S1 = 2 and ♯S2 = 9, such that any two admissible meromorphic functions f and g in Ω must be identical if f, g share S1, S2 I M in Ω.

Ograniczanie wyników

2 Open Mathematics

2 Wang H.

1 Xu H.-Y.

1 Zheng X.-M.

1 2016

1 2014

Wyniki wyszukiwania

Functions on adjacent vertex degrees of trees with given degree sequence

On meromorphic functions for sharing two sets and three sets inm-punctured complex plane