#### Document Type

Article

#### Publication Date

11-2014

#### Publication Title

Central European Journal of Mathematics

#### DOI

10.2478/s11533-014-0439-5

#### ISSN

2391-5455

#### Abstract

In this note we consider a discrete symmetric function f(x, y) where f(x; a) + f(y, b) ≥ f(y, a) + f(x, b) for any x ≥ y and a ≥ b, associated with the degrees of adjacent vertices in a tree. The extremal trees with respect to the corresponding graph invariant, defined as Σ _{uv∈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 Randić 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.

#### Recommended Citation

Wang, Hua.
2014.
"Functions on Adjacent Vertex Degrees of Trees with Given Degree Sequence."
*Central European Journal of Mathematics*, 12 (11): 1656-1663.
doi: 10.2478/s11533-014-0439-5

https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/288

## Comments

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This article was retrieved from Central European Journal of Mathematics.