5 problems

Character conjecture. For $lpha,\beta\rtf]\in(0,1)$ and feasible $n_1,n_2$, if $T_{n_1}$ and $T_{n_2}$ are dual fullerenes, then

Let $T_n$ be a dual fullerene graph and let $T_n^6$ be its hexagonal subgraph, for feasible $n$. A cut-partition of $T_n^6$ is the set of components generated by the stated cut-par…

Let $C_{56,622}$ and $C_{80,31924}$ denote the indicated fullerene graphs. A cut-partition of a hexagonal subgraph is the set of components generated by the stated cut-partition co…

Wiener complexity and diameter conjecture. The Wiener complexity and the diameter of fullerene graphs of an arbitrary order having the maximal Wiener index are given in Proposition…

Maximal Wiener index conjecture. If a fullerene graph of an arbitrary order has the maximal Wiener index, then it is a nanotubical fullerene graph with caps of types $a$--$d$, and…