Degree Sequence of Albertson and $\sigma$-Indices on Trees of Order $n⩾3$

In this paper, we presented a study of topological indices on trees, where we show a relationship with irregularity of Albertson index and minimum, maximum degrees $\delta ,\mathrm{\Delta }$ of graph $G$, where contribute vital roles in determining connection, shading, component incorporation, and realisability where well-known Albertson index as: $\mathrm{irr}(G)={\sum }_{uv\in E(G)}\mid d_u(G)-d_v(G)\mid$. The sigma index on trees that we introduced as $\sigma (T)=(d_1-1{)}^3+{\sum }_{i=1}^3(d_i-1)(d_i-2)+(d_3-1{)}^3$.