9 problems

Randić-index matching conjecture. If

Let $F$ be a graph and suppose ${\mathrm{ex}}(n,F)=\Theta(n^{2-\beta})$. For an integer $r$ with $r\beta=1$, let $R_r(n,F)$ be the maximum zeroth-order Randić index among $n$-verte…

Let $G$ be a graph, with Randić index $\operatorname{R}(G)$, diameter $\operatorname{d}(G)$, and order $\#V(G)$. Aouchiche–Hansen's conjectured bound. … This is a proposed lower bo…

Extension conjecture. Theorem 1 and Corollary 1 should still hold if

Let $G$ be a cactus with $k$ cycles and $b$ bridges; write $n$ for its number of vertices, $R$ for its Randić index, and $d$ for its diameter. A BC-tree is the block-cut tree of…

Let $G$ be a graph with $n$ vertices. Write $R=R(G)$ for its Randić index and $d$ for its diameter. Aouchiche's conjecture. The two bounds … and … should hold. These inequalities c…

Conjecture. The source introduces a conjecture concerning extremal graphs for the remaining parity combinations of $n$ and $k$, but the supplied statement is incomplete and does no…

Hansen and Lucas's conjecture.

Extremal Randić-index theorem.