TY - JOUR

T1 - Functions on Adjacent Vertex Degrees of Trees with Given Degree Sequence

AU - Wang, Hua

PY - 2014/11/1

Y1 - 2014/11/1

N2 - 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 (Formula presented.). 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.

AB - 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 (Formula presented.). 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.

KW - Degrees

KW - Function

KW - Index

KW - Trees

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

U2 - 10.2478/s11533-014-0439-5

DO - 10.2478/s11533-014-0439-5

M3 - Article

SN - 1895-1074

VL - 12

JO - Central European Journal of Mathematics

JF - Central European Journal of Mathematics

ER -