7 problems

Randić-index matching conjecture. If

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…

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…

Let $G$) be a graph. Write $R=R(G)$ for its Randić index and $r$ for its radius. An even path is a path with an even number of vertices. Fajtlowicz's conjecture. If $G$ is an even…

Let $G$ be a triangle-free graph, let $R(G)$ be its Randić index, and let $s^+(G)$ be the sum of the squares of the positive adjacency eigenvalues. Triangle-free Randić conjecture.…

Extremal Randić-index theorem.