10 problems

Hansen–Vukićević conjecture. For any simple finite graph $\mathcal{G}$,

Zagreb index comparison conjecture. If $G$ is a connected graph, then

Let $G$ be a graph with $n$ vertices, and let $cM_{2}(G)$ denote its complementary second Zagreb index, defined by … Here $K_m\vee\overline{K_{n-m}}$ is the join of the complete gr…

Let $G$ be a connected graph of order $n$, and let … where $d_u(G)$ is the degree of vertex $u$. Let $G^*$ be a graph attaining the maximum value of $cM_2$ among all connected grap…

For a connected graph $G$, let … where $d(u,v)$ is the distance between vertices $u$ and $v$, and $n_u(v)$ and $n_v(u)$ count vertices closer to $u$ and $v$, respectively, among th…

The complete multipartite extremal conjecture.

Let $T$ and $T'$ be any two trees with $n$ vertices. Wiener–Randić distance conjecture. It holds … The conjecture compares graph distance measures induced by the Wiener and Randić…

Let $\mathcal{R}(n)$ be the class of trees on $n$ vertices, and let $BP^0$ denote the Basic regression with minimum value $BP^{0*}_\mathcal{R}(n)$ over $\mathcal{R}(n)$. A tree is…

Harmonic index–radius conjecture. For all connected graphs $G$ except even paths,

Cao's strengthened conjecture. For any connected graph $G$ except even paths,