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A general algebraic characterization of extremal $Δ$-trees and $k$-cyclic graphs for degree-homogeneous VDB indices
We present a general algebraic method for maximizing a vertex-degree-based (VDB) topological index $TI(G) = \sum_{uv \in E(G)} f(d(u),d(v))$ over the class of $n$-vertex trees with a prescribed maximum degree $Δ\ge 3$. By expressing the edge multiplicities of the basis $\mathcal{B} = \{(1,Δ), (Δ,Δ)\
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