4 problems

Maximal $\alpha$-spectral-radius conjecture. If $G$ has the maximal $\alpha$-spectral radius among graphs in $\mathscr{B}(n,d)$, then

Let $B_2(n)$ denote the family of bicyclic graphs specified in the paper, and let $G\in B_2(n)$ have order $n\geq 11$. The Graovac-Ghorbani atom-bond connectivity index is denoted…

Let $\mathcal{B}'_n$ be the family of all bicyclic graphs on $n$ vertices, and let $G\in\mathcal{B}'_n$ have order $n\geq 8$. The Graovac-Ghorbani atom-bond connectivity index is d…

Let $P_n^{6,6}$ denote the bicyclic molecular graph of order $n$ corresponding to the alpha,beta diphenyl-polyene $C_6H_5(CH)_{n-12}C_6H_5$. Gutman–Vidović's conjecture. For $n=14$…