2 problems

Let $r\geq \frac52$ and $n\geq 2r+1$. Let $\overline{\Gamma}_{2r+1}$ be the digraph specified in the paper, and let $\overline{\Gamma}_{n,2r,i,s}$ denote the family obtained by the…

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…