Functions on adjacent vertex degrees of trees with given degree sequence

• Autorzy: Hua Wang
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Degrees; Function; Index; Trees

Kategorie tematyczne

• 05C05: Trees
• 05C07: Vertex degrees
• 05C35: Extremal problems

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 11
• Strony: 1656-1663

Daty

wydano

2014-11-01

online

2014-06-29

Twórcy

autor

Hua Wang

• Georgia Southern University,

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-014-0439-5