Sharp Upper Bounds on the Clar Number of Fullerene Graphs

Discussiones Mathematicae Graph Theory

Zhang Heping¹  Gao Yang² 

[1] School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, P.R. China;School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, P.R. China;

关键词: fullerene;    clar number;    clar set;    leapfrog transformation;    05c10;    05c62;    05c70;    92e10;   

DOI  :  10.7151/dmgt.2013

来源: DOAJ

【 摘 要 】

The Clar number of a fullerene graph with n vertices is bounded above by ⌊n/6⌋ − 2 and this bound has been improved to ⌊n/6⌋ − 3 when n is congruent to 2 modulo 6. We can construct at least one fullerene graph attaining the upper bounds for every even number of vertices n ≥ 20 except n = 22 and n = 30.

【 授权许可】

Unknown