A mathematical programming model for computing the Fries number of a fullerene

A fullerene graph is a cubic 3-connected plane graph with pentagonal and hexagonal faces. The Fries number of a fullerene is the maximum number of benzene-like faces over all possible perfect matchings. The Fries number and its associated Kekulé structure of a fullerene play a key role in molecular energy and stability. In this paper we propose a binary integer linear programming and a quadratic programming model for determining the Fries number of a fullerene. Moreover, interior point approach, as one of the most robust optimization techniques, is implemented to find the optimal solution of the proposed quadratic programming problem in moderate computing time.