8 problems

A fullerene nanodisc $D_r$ is a fullerene nanodisc indexed by an integer $r$. Type 1 conjecture. The fullerene nanodiscs $D_r$, for every integer $r\geq 2$, are Type 1. The conject…

Let $C_N$ be the class of fullerene isomers with $N$ atoms. Assume $N\neq 20,24,26,28,34$, $N\neq 10s$, and $N\neq 6k-4$, where $k\geq 5$ and $s\geq 2$. A nanotubical fullerene gra…

Let $C_N$ be the class of fullerene isomers with $N$ atoms. Suppose $N=6k-4\neq 10s$, where $k\geq 5$ and $s\geq 2$. A nanotubical fullerene has a tubular part and two caps, and ca…

Let $C_N$ be the class of fullerene isomers with $N$ atoms, and let $N=10k$ with $k\geq 2$. A nanotubical fullerene has a tubular part and two caps; a cap of type (a) is one of the…

Spectral characterization conjecture. (a) For all feasible $n\ne44$, two $C_n$-isomers are isomorphic if and only if they are cospectral with respect to $T_n$.

Fullerene saturation-number conjecture. There is a constant $C$ such that

Fullerene disk existence conjecture. Except for $(c,v)=(1,42)$, $(3,24)$, and $(5,22)$, a fullerene $c$-disk with $c\geq 1$ and $v$ vertices exists if and only if $v$ is even and

Let $H$ be a fullerene graph with $n$ vertices, and let $b(H)$ be the minimum number of edges whose removal makes $H$ bipartite. Doš​lić–Vukićević explicit conjecture. … This is pr…