ELIZABETH J. HARTUNG, Syracuse University
Fullerene Parameters: A Colorful Approach  [PDF]

The Fries number of a fullerene is the maximum number of benzene faces, while the Clar number is the maximum number of independent benzene faces. We will talk about classes of fullerenes over which the Clar number is known. We will also talk about relationships between the Clar and Fries number.

WENDY MYRVOLD, University of Victoria
Independent Sets of Fullerenes  [PDF]

A {\it fullerene} is an all carbon molecule that can be represented by a $3$-regular planar graph with face sizes five or six. A subset $S$ of the vertices of a graph forms an {\it independent set} if the vertices of $S$ are pairwise non-adjacent. This talk describes chemical applications for independent sets of fullerenes and algorithms for generating them.

NICO VAN CLEEMPUT, University of Ghent
CaGe - A Chemical and Abstract Graph Environment  [PDF]

CaGe (Chemical and Abstract Graph Environment) is an environment for generating and visualizing certain specialized classes of plane graphs with the emphasis on classes that are relevant in chemistry such as among others fullerenes, nanotubes and nanocones. CaGe can draw the graphs in 2 and 3 dimensions, can give an adjacency matrix and can output an unfolding of the 3 dimensional structure. Graphs can be exported in PDB and CML. CaGe is available at: http://caagt.ugent.be/CaGe

DONG YE, West Virginia University
Resonance in Fullerenes  [PDF]

A fullerene graph $G$ is a cubic plane graph with only pentagonal and hexagonal faces. A set $\mathcal H$ of disjoint hexagons is called a resonant set of $G$ if $G-\mathcal H$ has a perfect matching. A fullerene graph $G$ is $k$-resonant if any $i\le k$ disjoint hexagons form a resonant set of $G$. In this talk, we will survey some old and recent results about resonance of fullerene graphs, and propose some problems.

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