5 problems

Mostar index extremal graph conjecture. For any $n \ge 3$, the graph

Maximum Mostar index conjecture. The maximum Mostar index among graphs of order $n$ and maximum degree at most $\Delta$ is

Let $m$ be the size of a bicyclic graph, and let $B_m$ and $B^5_m$ denote the bicyclic graphs shown in the source's Figures X and Y, respectively. Liu–Shan–Xu's conjecture. If $m$…

Let $G$ be a finite simple graph of order $n$, where $n$ is a multiple of $3$. For integers $k$ and $n-k$, let $S_{k,n-k}$ be the split graph obtained from the disjoint union of a…

Došljić–Miklavčič–Tizuka conjecture. The complete bipartite graph $K_{n/3,2n/3}$ has maximum Mostar index among all bipartite graphs of order $n$, and $S_{n/3,2n/3}$ has maximum Mo…