2025/01/15 by Green, Linda, Sreelesh, Yadunand, Arora, Saanvi
#05C10 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2501.09170
A (3, 6)-fullerene is a cubic planar graph whose faces all have 3 or 6 sides. We give an exact count of the number of (3, 6)-fullerenes for any given number of vertices. We also enumerate (3,6)-fullerenes with mirror symmetry, with 3-fold rotational symmetry, and with both types of symmetry. The counts are given in terms of the prime factorization of the number of vertices, by considering solutions to the quadratic equation x2 + x + 1 = 0 modulo the primes in this prime factorization.