Forcing and Anti-Forcing Numbers of (3,6)-Fullerenes

摘要

Let G be a connected graph with at least one perfect matching. The forcing number of G is the smallest number of edges simultaneously contained in a unique perfect matching of G, denoted by f(G). The anti-forcing number of G is the smallest number of edges whose removal from G results in a subgraph with a unique perfect matching, denoted by of (G). In this paper, we obtain that for a (3, 6)-fullerene graph G, f (G) >= 1 and af(G) >= 2, and any equality holds if and only if it either has connectivity 2 or is isomorphic to K-4. Further we mainly determine all the (3, 6)-fullerenes with the anti-forcing number 3.