# On the Anti-Forcing Number of Fullerene Graphs

###
Heping Zhang

Lanzhou University

PDF

**Minisymposium:**
CHEMICAL GRAPH THEORY

**Content:**
The anti-forcing number of a
connected graph $G$ is the smallest number of edges such that the
remaining graph obtained by deleting these edges has a unique
perfect matching. In this paper, we show that the
anti-forcing number of every fullerene has at least four. We give a procedure to construct all fullerenes whose anti-forcing numbers achieve the lower bound four. Furthermore, we show that, for every
even $n\geq 20$ ($n\neq 22, 26$), there exists a
fullerene with $n$ vertices that has the anti-forcing number four, and the fullerene with 26 vertices has the anti-forcing number five.