9 problems

Let $G$ be a graph and let $H_{a,b}$ denote the family of graphs introduced in the paper, where $a,b$ are non-negative integers. Classification conjecture for extremal graphs. If ……

Let $G=(V,E)$ be a $5$-regular Ricci-flat graph. A graph is of Cartesian product type if it is the Cartesian product of a Ricci-flat $3$-regular graph and a Ricci-flat $2$-regular…

Let $G$ be a graph of order $n$, and let $K_n$, $K_{1,n-1}$, $K(m;n_1,n_2,\ldots,n_m)$, and $Ct(3;n_1,0,n_3)$ denote the graph families used in the paper. Order-equality classifica…

Bang–Koolen's classification conjecture. Any such graph is a Johnson graph, a Hamming graph, a Grassmann graph, a bilinear forms graph, or has a number of vertices bounded by a fun…

Let the families listed above be the fifteen families of planar graphs constructed in the paper with exactly two disparate faces. Classification conjecture. These families are the…

Ten-vertex classification conjecture. The only graphs $G$ on 10 vertices with $c_L(G)=3$ are either the Petersen graph, or a copy of $R_3$ with an additional vertex $v$ whose degre…

Middle-level graph conjecture. The graph $G$ is a middle-level graph.

Let $\mathcal{G}=\{G_i\}_{i=1}^{\infty}$ be an infinite family of simple graphs such that $G_i$ is a proper induced subgraph of $G_j$ for all $i<j$. Eventual family conjecture. Eit…

For $k\geq1$, let … and let $\mathcal{T}_{\delta}^*(G)$ denote the set of induced subgraphs of one graph in $\mathcal{T}_{\delta}(G)$. Finite classification conjecture. For every…