Structure of resonance graphs of some carbon nanotubes
Presented by Prof. Petra ŽIGERT PLETERšEK
Type: Oral presentation
Carbon nanotubes were discovered almost 30 years ago and their unique structure explains their unusual properties such as conductivity and strength. Their aromaticity can be mathematical modeled with resonance graphs, where vertices are perfect matchings t.i. Kekule structures of a nanotube, and two vertices are adjacent, if their symmetric difference is a hexagon. Lucas cubes are a class of graphs based on a Fibonacci string that were introduces in the last 15 years as models for interconnection networks. The vertex set of a Lucas cube Ln is the set of all binary strings of length n without consecutive 1's and 1 in the first and the last bit. Two vertices of Lucas cube are adjacent if their strings differ in exactly one bit. We will show that the resonance graphs of some class of carbon nanotubes are connected to Lucas cubes and their amalgams.