Computing he Clar number of fulleren graphs

A (3,6)-fullerene G is a plane cubic graph whose faces are only triangles and hexagons. It follows from Euler’sformula that the number of triangles is four . A matching of a graph G is a set of pair-wise disjoint edges M of G , and aperfect matching or Kekulé structure is a matching M covering all vertices of G . A cycle of G is M-alternating if itsedges appear alternately in and off M.Let Fn be a fullerene graph with n vertices. A set H of disjoint hexagons of Fn is called a resonant pattern (or sextetpattern) if Fn has a perfect matching M such that each hexagon in H is M-alternating. The maximum cardinality of allsextet patterns of Fn is the Clar number of Fn . The aim of thesis study is to study the Kekulé structure and the Clarnumber of (3,6)- fullerenes. We also compute the Clar number of some infinite family of fullerenes.

Keywords:

Kekulé structure , sextet pattern , Clar number , fullerene graphs