By a fullerene, we mean a trivalent plane graph Γ = (V,E, F ) with only hexagonal and pentagonal faces. It follows easily from Euler’s Formula that each fullerene has exactly 12 pentagonal faces. The… (More)

We explore the structure of the maximum vertex independence sets in fullerenes: plane trivalent graphs with pentagonal and hexagonal faces. At the same time, we will consider benzenoids: plane graphs… (More)

A simple (non overlapping) region of the hexagonal tessellation of the plane is uniquely determined by its boundary. This seems also to be true for “regions” that curve around and have a simple… (More)

We explore the relationship between Kekulé structures and maximum face independence sets in fullerenes: plane trivalent graphs with pentagonal and hexagonal faces. For the class of leap-frog… (More)

A cut-and-paste approach using a family of structurally similar ‘growth patches’ (pairs of non-isomorphic patches with the same boundary but containing different numbers of vertices) allows formal… (More)

Large carbon molecules, discovered at the end of the last century, are called fullerenes. The most famous of these, C60 has the structure of the soccer ball: the seams represent chemical bonds and… (More)