Bounds on Trees with Topological Indices Among Degree Sequence

In this paper, we investigate The relationship between the Albertson index and the first Zagreb index for trees. For a tree $T=(V,E)$ with $n=|V|$ vertices and $m=|E|$ edges, we provide several bounds and exact formulas for these two topological indices, and we show that the Albertson index (T) and the first Zagreb index M₁(T) satisfy the association \[ irr(T)=d_1^2+d_n^2+(n-2)(Δ + δ/2)^2+∑ᵢ₌₂ⁿ⁻¹ d_i+d_n - d_1-2n-2.\] Our goal of this paper is provide a topological indices, Albertson index, Sigma index among a degree sequence D=(d₁,,dₙ) where it is non-increasing and non-decreasing of tree T.