The molecular structures of porphyrinoid cages were obtained by constructing small
polyhedral graphs whose vertices have degree-4. The initial structures were then fully …

Magnetically induced current densities (MICDs) of Zn-porphyrinoid nanostructures have
been studied at the density functional theory level using the B3LYP functional and the def2 …

Combinatorial techniques based on Sheehan's modification of Pόlya's theorem and Mȍbius
inversion technique together with character cycle indices are applied to face colorings of …

A Pogorelov polytope is a combinatorial simple 3-polytope realizable in the Lobachevsky
(hyperbolic) space as a bounded right-angled polytope. These polytopes are exactly simple …

We have developed combinatorial generation function methods that combine Mȍbius
inversion and character cycle indices for the enumeration of stereo, position and chiral …

Can we solve electronic wave equations absent a coordinate system? The question arises
from the wish to treat polyhedral molecules such as fullerenes as two-dimensional closed …

Abstract After Curl, Kroto and Smalley were awarded 1996 the Nobel Prize in chemistry,
fullerenes have been subject of much research. One part of that research is the prediction of …

We present a massively parallel lockstep algorithm for dualizing large numbers of surface
triangulation graphs, and an effective implementation for CPU, GPU and multi-GPU. The …

Fullerenes are hollow carbon molecules where each atom is connected to exactly three
other atoms, arranged in pentagonal and hexagonal rings. Mathematically, they can be …

We present a complete list of three-dimensional structures corresponding to all cubic
polyhedral graphs with the number of vertices up to 24, which have only square, pentagonal …