论文标题
关于富勒烯双曲线体积的相关性与其性质
On correlation of hyperbolic volumes of fullerenes with their properties
论文作者
论文摘要
我们观察到富勒烯图是多面体的一骨骨骼，在双曲线3维空间中，所有二面角可以用等于$π/2 $的所有二面角度实现。这种多面体的最重要不变之一是其体积。我们将此卷称为富勒烯的双曲线体积。众所周知，化合物图的某些拓扑指数是强的描述符，并且与化学性质相关。我们证明，富勒烯的双曲线体积与很少的重要拓扑指数相关，因此，双曲线体积也可以用作化学描述符。富勒烯的双曲线体积及其维纳指数之间的相关性表明，对双曲线多面体的体积很少。这些猜想已确认富勒烯的初始清单。
We observe that fullerene graphs are one-skeletons of polyhedra, which can be realized with all dihedral angles equal to $π/2$ in a hyperbolic 3-dimensional space. One of the most important invariants of such a polyhedron is its volume. We are referring this volume as a hyperbolic volume of a fullerene. It is known that some topological indices of graphs of chemical compounds serve as strong descriptors and correlate with chemical properties. We demonstrate that hyperbolic volume of fullerenes correlates with few important topological indices and so, hyperbolic volume can serve as a chemical descriptor too. The correlation between hyperbolic volume of fullerene and its Wiener index suggested few conjectures on volumes of hyperbolic polyhedra. These conjectures are confirmed for the initial list of fullerenes.
